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Last updated on June 2nd, 2025

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Cube of 507

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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 507.

Cube of 507 for Indonesian Students
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Cube of 507

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 multiplied by itself three times results in a negative number. The cube of 507 can be written as 507³, which is the exponential form. Or it can also be written in arithmetic form as, 507 × 507 × 507.

cube of 507

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How to Calculate the Value of Cube of 507

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.

 

  • 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 numbers by combining them through repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.

 

Step 1: Write down the cube of the given number.

507³ = 507 × 507 × 507

 

Step 2: You get 130,515,843 as the answer.

 

Hence, the cube of 507 is 130,515,843.

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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 507 into two parts.

Let a = 500 and b = 7, so a + b = 507

 

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

 

Step 3: Calculate each term a³= 500³ , 3a²b = 3 × 500² × 7 , 3ab² = 3 × 500 × 7² , b³ = 7³

 

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(500 + 7)³ = 500³ + 3 × 500² × 7 + 3 × 500 × 7² + 7³ 507³

= 125,000,000 + 5,250,000 + 73,500 + 343 507³

= 130,515,843

 

Step 5: Hence, the cube of 507 is 130,515,843.

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Using a Calculator

To find the cube of 507 using a calculator, input the number 507 and use the cube function (if available) or multiply 507 × 507 × 507. This operation calculates the value of 507³, resulting in 130,515,843. 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 then 7

 

Step 3: If the calculator has a cube function, press it to calculate 507³.

 

Step 4: If there is no cube function on the calculator, simply multiply 507 three times manually.

 

Step 5: The calculator will display 130,515,843.

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Tips and Tricks for the Cube of 507

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 507

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, 507 × 507 and not 507 × 507 × 507. Always remember that 507³ = 507 × 507 × 507.

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Solved Examples on Cube of 507

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Problem 1

What is the cube and cube root of 507?

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The cube of 507 is 130,515,843 and the cube root of 507 is approximately 7.986.

Explanation

First, let’s find the cube of 507.

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

So, we get 507³ = 130,515,843

Next, we must find the cube root of 507.

We know that the cube root of a number ‘x’ is such that ³√x = y, where ‘x’ is the given number, and y is the cube root value of the number.

So, we get ³√507 ≈ 7.986

Hence, the cube of 507 is 130,515,843 and the cube root of 507 is approximately 7.986.

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Problem 2

If the side length of a cube is 507 cm, what is the volume?

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The volume is 130,515,843 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 507 for the side length: V = 507³ = 130,515,843 cm³.

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Problem 3

How much larger is 507³ than 407³?

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507³ – 407³ = 88,514,843.

Explanation

First find the cube of 507, which is 130,515,843.

Next, find the cube of 407, which is 42,001,000.

Now, find the difference between them using the subtraction method: 130,515,843 – 42,001,000 = 88,514,843.

Therefore, 507³ is 88,514,843 larger than 407³.

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Problem 4

If a cube with a side length of 507 cm is compared to a cube with a side length of 107 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 507 cm is 130,515,843 cm³.

Explanation

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

Cubing 507 means multiplying 507 by itself three times:

507 × 507 = 257,049, and then 257,049 × 507 = 130,515,843.

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

Therefore, the volume of the cube is 130,515,843 cm³.

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Problem 5

Estimate the cube of 506.9 using the cube of 507.

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The cube of 506.9 is approximately 130,515,843.

Explanation

First, identify the cube of 507, which is 507³ = 130,515,843.

Since 506.9 is only a tiny bit less than 507, the cube of 506.9 will be almost the same as the cube of 507.

The cube of 506.9 is approximately 130,515,843 because the difference between 506.9 and 507 is very small.

So, we can approximate the value as 130,515,843.

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FAQs on Cube of 507

1.What are the perfect cubes up to 507?

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2.How do you calculate 507³?

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3.What is the meaning of 507³?

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4.What is the cube root of 507?

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5.Is 507 a perfect cube?

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

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7.How can cultural or local activities in Indonesia support learning Algebra topics such as Cube of 507?

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8.How do technology and digital tools in Indonesia support learning Algebra and Cube of 507?

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

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Important Glossaries for Cube of 507

  • 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, 2³ represents 2 × 2 × 2 equals 8.

     
  • Perfect Cube: A number that can be expressed as the product of three equal integers.

     
  • Cube Root: A number that when multiplied by itself three times gives the original number, represented as ³√x.
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About BrightChamps in Indonesia

At BrightChamps, algebra is more than just symbols—it opens up a world of possibilities! We are passionate about helping children throughout Indonesia develop key math skills, with today’s spotlight on the Cube of 507 and a special focus on cubes—in an engaging, clear, and enjoyable way. Whether your child is figuring out the speed of a roller coaster at Dunia Fantasi, keeping track of scores at a local badminton match, or managing their allowance for the latest gadgets, mastering algebra gives them the confidence to tackle everyday problems. Our interactive sessions make learning both fun and simple. Because kids in Indonesia have different learning styles, we adjust our methods to suit each child’s needs. From Jakarta’s busy streets to Bali’s stunning beaches, BrightChamps brings algebra to life, making it exciting and meaningful across Indonesia. 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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