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Last updated on June 3rd, 2025

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Cube of 505

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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 505.

Cube of 505 for Filipino Students
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Cube of 505

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 505 can be written as 5053, which is the exponential form. Or it can also be written in arithmetic form as 505 × 505 × 505.

cube of 505

 

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How to Calculate the Value of Cube of 505

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 (a^3), 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.

 

  • By Multiplication Method
     
  • Using a Formula
     
  • 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.

5053 = 505 × 505 × 505

 

Step 2: You get 128,012,625 as the answer.

 

Hence, the cube of 505 is 128,012,625.

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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 505 into two parts, as 500 and 5. Let a = 500 and b = 5, so a + b = 505

 

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

 

Step 3: Calculate each term a3 = 5003 , 3a2b = 3 × 5002 × 5 , 3ab2 = 3 × 500 × 52 , b3 = 53

 

Step 4: Add all the terms together:

(a + b)3 = a3 + 3a2b + 3ab2 + b3 

(500 + 5)3 = 5003 + 3 × 500× 5 + 3 × 500 × 52 + 53

5053 = 125,000,000 + 3,750,000 + 37,500 + 125 5053

= 128,012,625

 

Step 5: Hence, the cube of 505 is 128,012,625.

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Using a Calculator

To find the cube of 505 using a calculator, input the number 505 and use the cube function (if available) or multiply 505 × 505 × 505. This operation calculates the value of 5053, resulting in 128,012,625. It’s a quick way to determine the cube without manual computation.

 

Step 1: Ensure the calculator is functioning properly.

 

Step 2: Press 5 followed by 0, and then 5

 

Step 3: If the calculator has a cube function, press it to calculate 5053.

 

Step 4: If there is no cube function on the calculator, simply multiply 505 three times manually.

 

Step 5: The calculator will display 128,012,625.

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Tips and Tricks for the Cube of 505

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 505

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, 505 × 505 and not 505 × 505 × 505. Always remember that 5053 = 505 × 505 × 505.

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Solved Examples on Cube of 505

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Problem 1

What is the cube and cube root of 505?

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The cube of 505 is 128,012,625 and the cube root of 505 is approximately 7.937.

Explanation

First, let’s find the cube of 505.

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 5053 = 128,012,625

Next, we must find the cube root of 505

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 ∛505 ≈ 7.937

Hence the cube of 505 is 128,012,625 and the cube root of 505 is approximately 7.937.

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Problem 2

If the side length of the cube is 505 cm, what is the volume?

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The volume is 128,012,625 cm³.

Explanation

Use the volume formula for a cube V = Side3.

Substitute 505 for the side length: V = 5053 = 128,012,625 cm³.

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Problem 3

How much larger is 505^3 than 405^3?

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5053 – 4053 = 76,521,625.

Explanation

First, find the cube of 5053, that is 128,012,625

Next, find the cube of 4053, which is 51,491,000

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

128,012,625 – 51,491,000 = 76,521,625

Therefore, 5053 is 76,521,625 larger than 4053.

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Problem 4

If a cube with a side length of 505 cm is compared to a cube with a side length of 105 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 505 cm is 128,012,625 cm³

Explanation

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

Cubing 505 means multiplying 505 by itself three times: 505 × 505 = 255,025, and 255,025 × 505 = 128,012,625.

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

Therefore, the volume of the cube is 128,012,625 cm³.

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Problem 5

Estimate the cube 504.9 using the cube 505.

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The cube of 504.9 is approximately 128,012,625.

Explanation

First, identify the cube of 505.

The cube of 505 is 5053 = 128,012,625.

Since 504.9 is only a tiny bit less than 505, the cube of 504.9 will be almost the same as the cube of 505.

The cube of 504.9 is approximately 128,012,625 because the difference between 504.9 and 505 is very small.

So, we can approximate the value as 128,012,625.

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FAQs on Cube of 505

1.What are the perfect cubes up to 505?

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2.How do you calculate 505^3?

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3.What is the meaning of 505^3?

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4.What is the cube root of 505?

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5.Is 505 a perfect cube?

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

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7.How can cultural or local activities in Philippines support learning Algebra topics such as Cube of 505?

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8.How do technology and digital tools in Philippines support learning Algebra and Cube of 505?

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

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Important Glossaries for Cube of 505

  • Binomial Formula: 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: 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, 23represents 2 × 2 × 2 equals 8.

     
  • Volume: The amount of space occupied by a 3-dimensional object, calculated by cubing the side length for a cube. 

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

At BrightChamps, algebra is more than just numbers—it’s the key to unlocking many opportunities! We dedicate ourselves to helping kids across the Philippines grasp important math concepts, including today’s focus on the Cube of 505 with a special emphasis on cubes—in an engaging, clear, and fun way. Whether your child is calculating the speed of a roller coaster at Enchanted Kingdom, following basketball scores, or managing their allowance to buy new gadgets, mastering algebra builds their confidence for everyday challenges. Our interactive lessons make math learning fun and easy. Because kids in the Philippines learn in diverse ways, we tailor our approach to each child’s unique style. From Manila’s busy streets to Palawan’s stunning islands, BrightChamps makes algebra exciting and relatable throughout the Philippines. Let’s make cubes a fun part of every child’s math adventure!
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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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