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Last updated on June 2nd, 2025

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Cube of 663

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When a number is multiplied by itself thrice, the resultant number is called the cube of a number. Cubing is used while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 663.

Cube of 663 for Omani Students
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Cube of 663

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 a negative number by itself three times results in a negative number.

 

The cube of 663 can be written as 663³, which is the exponential form. Or it can also be written in arithmetic form as, 663 × 663 × 663.

cube of 663

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How to Calculate the Value of Cube of 663

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

 

  1. By Multiplication Method
  2. Using a Formula
  3. Using a Calculator
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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. 663³ = 663 × 663 × 663

 

Step 2: You get 291,420,087 as the answer. Hence, the cube of 663 is 291,420,087.

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Using a Formula (a³)

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 663 into two parts, as 600 and 63. Let a = 600 and b = 63, so a + b = 663

 

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

 

Step 3: Calculate each term a³= 600³ 3a²b = 3 × 600² × 63 3ab² = 3 × 600 × 63² b³ = 63³

 

Step 4: Add all the terms together:

 

(a + b)³ = a³ + 3a²b + 3ab² + b³

 

(600 + 63)³ = 600³ + 3 × 600² × 63 + 3 × 600 × 63² + 63³

 

663³ = 216,000,000 + 68,040,000 + 7,155,600 + 250,047

 

663³ = 291,420,087

 

Step 5: Hence, the cube of 663 is 291,420,087.

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Using a Calculator

To find the cube of 663 using a calculator, input the number 663 and use the cube function (if available) or multiply 663 × 663 × 663. This operation calculates the value of 663³, resulting in 291,420,087. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Enter 6 followed by 6 and 3

 

Step 3: If the calculator has a cube function, press it to calculate 663³.

 

Step 4: If there is no cube function on the calculator, simply multiply 663 three times manually.

 

Step 5: The calculator will display 291,420,087.

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Tips and Tricks for the Cube of 663

  • 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.
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Common Mistakes to Avoid When Calculating the Cube of 663

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

Mistake 1

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Incorrect Multiplication

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Kids might multiply the numbers only twice. That is, 663 × 663 and not 663 × 663 × 663. Always remember that 663³ = 663 × 663 × 663.

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Solved Examples on Cube of 663

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Problem 1

What is the cube and cube root of 663?

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The cube of 663 is 291,420,087, and the cube root of 663 is approximately 8.749.

Explanation

First, let’s find the cube of 663.

 

We know that the cube of a number, such that x³ = y, where x is the given number, and y is the cubed value of that number.

 

So, we get 663³ = 291,420,087.

 

Next, we must find the cube root of 663.

 

We know that the cube root of a number ‘x’, such that ∛x = y, where x is the given number, and y is the cube root value of the number.

 

So, we get ∛663 ≈ 8.749.

 

Hence, the cube of 663 is 291,420,087, and the cube root of 663 is approximately 8.749.

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Problem 2

If the side length of the cube is 663 cm, what is the volume?

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The volume is 291,420,087 cm³.

Explanation

Use the volume formula for a cube V= Side³.

 

Substitute 663 for the side length: V = 663³ = 291,420,087 cm³.

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Problem 3

How much larger is 663³ than 600³?

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663³ – 600³ = 75,420,087.

Explanation

First, find the cube of 663³, that is 291,420,087.

 

Next, find the cube of 600³, which is 216,000,000.

 

Now, find the difference between them using the subtraction method.

 

291,420,087 – 216,000,000 = 75,420,087.

 

Therefore, 663³ is 75,420,087 larger than 600³.

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Problem 4

If a cube with a side length of 663 cm is compared to a cube with a side length of 63 cm, how much larger is the volume of the larger cube?

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The volume of the cube with a side length of 663 cm is 291,420,087 cm³.

Explanation

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

 

Cubing 663 means multiplying 663 by itself three times: 663 × 663 = 439,569, and then 439,569 × 663 = 291,420,087.

 

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

 

Therefore, the volume of the cube is 291,420,087 cm³.

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Problem 5

Estimate the cube of 662.9 using the cube of 663.

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The cube of 662.9 is approximately 291,420,087.

Explanation

First, identify the cube of 663.

 

The cube of 663 is 663³ = 291,420,087.

 

Since 662.9 is only a tiny bit less than 663, the cube of 662.9 will be almost the same as the cube of 663.

 

The cube of 662.9 is approximately 291,420,087 because the difference between 662.9 and 663 is very small.

 

So, we can approximate the value as 291,420,087.

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FAQs on Cube of 663

1.What are the perfect cubes up to 663?

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2.How do you calculate 663³?

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3.What is the meaning of 663³?

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4.What is the cube root of 663?

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5.Is 663 a perfect cube?

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

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7.How can cultural or local activities in Oman support learning Algebra topics such as Cube of 663?

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8.How do technology and digital tools in Oman support learning Algebra and Cube of 663?

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

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Important Glossaries for Cube of 663

  • 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.

 

  • Perfect Cube: A number that can be expressed as the cube of an integer.

 

  • Cube Root: The value that, when cubed, gives the original number. For example, the cube root of 27 is 3.
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About BrightChamps in Oman

At BrightChamps, algebra is more than just digits—it’s a path to endless opportunities! We focus on helping children across Oman develop important math skills, like today’s focus on the Cube of 663, especially understanding cubes—in a fun, engaging, and easy-to-follow way. Whether your child is calculating how fast a roller coaster moves at Oman’s Dreamland Aqua Park, keeping track of scores at local sports events, or managing their allowance for the latest gadgets, mastering algebra gives them the confidence to meet everyday challenges. Our interactive lessons make math learning enjoyable and straightforward. Because children in Oman learn in diverse ways, we tailor our teaching to match each child’s style. From the vibrant city of Muscat to Oman’s natural landscapes, BrightChamps brings algebra to life, making it exciting and relatable throughout Oman. Let’s make cubes a fun part of every child’s math journey!
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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.

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Fun Fact

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

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