BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon115 Learners

Last updated on May 30th, 2025

Math Whiteboard Illustration

Cube of 401

Professor Greenline Explaining Math Concepts

When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 401.

Cube of 401 for Saudi Students
Professor Greenline from BrightChamps

Cube of 401

A cube number is a value obtained by raising a number to the power of 3, or by multiplying the number by itself three times.

 

When you cube a positive number, the result is always positive.

 

When you cube a negative number, the result is always negative.

 

This is because multiplying a negative number by itself three times results in a negative number.

 

The cube of 401 can be written as 4013, which is the exponential form.

 

Or it can also be written in arithmetic form as 401 × 401 × 401.

cube of 401

Professor Greenline from BrightChamps

How to Calculate the Value of Cube of 401

In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a3), or by using a calculator. These three methods will help students to cube the numbers faster and easier without feeling confused or stuck while evaluating the answers.

 

  • By Multiplication Method
     
  • Using a Formula (a3)
     
  • Using a Calculator
Professor Greenline from BrightChamps

By Multiplication Method

The multiplication method is a process in mathematics used to find the product of two numbers or quantities by combining them through repeated addition. It is a fundamental operation that forms the basis for more complex mathematical concepts.

 

Step 1: Write down the cube of the given number. 4013 = 401 × 401 × 401

 

Step 2: Calculate the product to get 64,480,601 as the answer. Hence, the cube of 401 is 64,480,601.

Professor Greenline from BrightChamps

Using a Formula (a^3)

The formula (a + b)3 is a binomial formula for finding the cube of a number. The formula is expanded as a3 + 3a2b + 3ab2 + b3.

 

Step 1: Split the number 401 into two parts. Let a = 400 and b = 1, so a + b = 401

 

Step 2: Now, apply the formula (a + b)3 = a3 + 3a2b + 3ab2 + b3

 

Step 3: Calculate each term a3 = 4003 3a2b = 3 × 4002 × 1 3ab2 = 3 × 400 × 12 b3 = 13

 

Step 4: Add all the terms together: (a + b)3 = a3 + 3a2b + 3ab2 + b3 (400 + 1)3 = 4003 + 3 × 4002 × 1 + 3 × 400 × 12 + 13 4013 = 64,000,000 + 480,000 + 1,200 + 1 4013 = 64,480,601

 

Step 5: Hence, the cube of 401 is 64,480,601.

Professor Greenline from BrightChamps

Using a Calculator

To find the cube of 401 using a calculator, input the number 401 and use the cube function (if available) or multiply 401 × 401 × 401. This operation calculates the value of 4013, resulting in 64,480,601. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Press 4 followed by 0 and 1

 

Step 3: If the calculator has a cube function, press it to calculate 4013.

 

Step 4: If there is no cube function on the calculator, simply multiply 401 three times manually.

 

Step 5: The calculator will display 64,480,601.

Professor Greenline from BrightChamps

Tips and Tricks for the Cube of 401

The cube of any even number is always even, while the cube of any odd number is always odd.

The product of two or more perfect cube numbers is always a perfect cube.

A perfect cube can always be expressed as the product of three identical groups of equal prime factors.

Max Pointing Out Common Math Mistakes

Common Mistakes to Avoid When Calculating the Cube of 401

There are some typical errors that students might make during the process of cubing a number. Let us take a look at five of the major mistakes that students might make:

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Incorrect Multiplication

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

Students might multiply the numbers only twice. That is, 401 × 401 and not 401 × 401 × 401. Always remember that 4013 = 401 × 401 × 401.

Max from BrightChamps Saying "Hey"

Solved Examples on Cube of 401

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

What is the cube and cube root of 401?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The cube of 401 is 64,480,601 and the cube root of 401 is approximately 7.368.

Explanation

First, let’s find the cube of 401.

We know that the cube of a number x is x3.

So, we get 4013 = 64,480,601. Next, we must find the cube root of 401.

We know that the cube root of a number x is ∛x.

So, we get ∛401 ≈ 7.368.

Hence, the cube of 401 is 64,480,601 and the cube root of 401 is approximately 7.368.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

If the side length of a cube is 401 cm, what is the volume?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The volume is 64,480,601 cm³.

Explanation

Use the volume formula for a cube V = Side3.

Substitute 401 for the side length: V = 4013 = 64,480,601 cm³.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

How much larger is 401^3 than 400^3?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

4013 – 4003 = 481,201.

Explanation

First find the cube of 401, which is 64,480,601.

Next, find the cube of 400, which is 64,000,000.

Now, find the difference between them using the subtraction method. 64,480,601 – 64,000,000 = 481,201.

Therefore, 401^3 is 481,201 larger than 4003.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

If a cube with a side length of 401 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The volume of the cube with a side length of 401 cm is 64,480,601 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object).

Cubing 401 means multiplying 401 by itself three times: 401 × 401 = 160,801, and then 160,801 × 401 = 64,480,601.

The unit of volume is cubic centimeters (cm³) because we are calculating the space inside the cube.

Therefore, the volume of the cube is 64,480,601 cm³.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Estimate the cube of 400.1 using the cube of 401.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The cube of 400.1 is approximately 64,480,601.

Explanation

First, identify the cube of 401.

The cube of 401 is 4013 = 64,480,601.

Since 400.1 is only a tiny bit less than 401, the cube of 400.1 will be almost the same as the cube of 401.

The cube of 400.1 is approximately 64,480,601 because the difference between 400.1 and 401 is very small.

So, we can approximate the value as 64,480,601.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQs on Cube of 401

1.What are the perfect cubes up to 401?

Math FAQ Answers Dropdown Arrow

2.How do you calculate 401^3?

Math FAQ Answers Dropdown Arrow

3.What is the meaning of 401^3?

Math FAQ Answers Dropdown Arrow

4.What is the cube root of 401?

Math FAQ Answers Dropdown Arrow

5.Is 401 a perfect cube?

Math FAQ Answers Dropdown Arrow

6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Cube of 401?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Saudi Arabia support learning Algebra and Cube of 401?

Math FAQ Answers Dropdown Arrow

9.Does learning Algebra support future career opportunities for students in Saudi Arabia?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for Cube of 401

  • Binomial Formula: It is an algebraic expression used to expand the powers of a number, written as (a + b)n, where ‘n’ is a positive integer raised to the base. The formula is used to find the square and cube of a number.

 

  • Cube of a Number: Multiplying a number by itself three times is called the cube of a number.

 

  • Exponential Form: It is a way of expressing numbers using a base and an exponent (or power), where the exponent value indicates how many times the base is multiplied by itself. For example, 23 represents 2 × 2 × 2 equals 8.

 

  • Cube Root: The value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2.

 

  • Volume of a Cube: The amount of space inside a cube, calculated as the cube of its side length.
Professor Greenline from BrightChamps

About BrightChamps in Saudi Arabia

At BrightChamps, algebra means more than just figures—it unlocks endless opportunities! Our mission is to support kids all across Saudi Arabia in learning key math concepts, including today’s focus on the Cube of 401 with a special highlight on cubes—in a fun, clear, and engaging way. Whether your child is figuring out the speed of a roller coaster at Riyadh’s Al Hokair Land, following scores at a local football match, or budgeting their allowance for the latest gadgets, mastering algebra boosts their confidence for everyday challenges. Our interactive lessons make learning simple and fun. Since kids in Saudi Arabia have different ways of learning, we customize our approach to each child’s style. From Riyadh’s bustling streets to Jeddah’s historic sites, BrightChamps brings algebra to life, making it exciting and relevant across Saudi Arabia. Let’s make cubes a fun part of every child’s math journey!
Math Teacher Background Image
Math Teacher Image

Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom