Cube of 107
2026-02-28 10:29 Diff
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Last updated on August 5, 2025

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 the cube of 107.

Cube of 107

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 107 can be written as 107³, which is the exponential form.

Or it can also be written in arithmetic form as 107 × 107 × 107.

How to Calculate the Value of the Cube of 107

To check whether a number is a cube number or not, we can use the following three methods: the 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  (a3)
     
  • Using a Calculator

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. 107³ = 107 × 107 × 107

Step 2: You get 1,224,463 as the answer.

Hence, the cube of 107 is 1,224,463.

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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 107 into two parts. Let a = 100 and b = 7, so a + b = 107

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

Step 3: Calculate each term a³ = 100³ 3a²b = 3 × 100² × 7 3ab² = 3 × 100 × 7² b³ = 7³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (100 + 7)³ = 100³ + 3 × 100² × 7 + 3 × 100 × 7² + 7³ 107³ = 1,000,000 + 210,000 + 14,700 + 343 107³ = 1,224,463

Step 5: Hence, the cube of 107 is 1,224,463.

Using a Calculator

To find the cube of 107 using a calculator, input the number 107 and use the cube function (if available) or multiply 107 × 107 × 107. This operation calculates the value of 107³, resulting in 1,224,463. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 1 followed by 0 and 7.

Step 3: If the calculator has a cube function, press it to calculate 107³.

Step 4: If there is no cube function on the calculator, simply multiply 107 three times manually.

Step 5: The calculator will display 1,224,463.

Tips and Tricks for the Cube of 107

  • 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.

Common Mistakes to Avoid When Calculating the Cube of 107

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:

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Problem 1

What is the cube and cube root of 107?

Okay, lets begin

The cube of 107 is 1,224,463 and the cube root of 107 is approximately 4.732.

Explanation

First, let’s find the cube of 107.

We know that the cube of a number is expressed as x³ = y

Where x is the given number, and y is the cubed value of that number.

So, we get 107³ = 1,224,463.

Next, we must find the cube root of 107.

We know that the cube root of a number ‘x’ is expressed as ∛x = y

Where ‘x’ is the given number, and y is the cube root value of the number.

So, we get ∛107 ≈ 4.732.

Hence, the cube of 107 is 1,224,463 and the cube root of 107 is approximately 4.732.

Well explained 👍

Problem 2

If the side length of the cube is 107 cm, what is the volume?

Okay, lets begin

The volume is 1,224,463 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 107 for the side length: V = 107³ = 1,224,463 cm³.

Well explained 👍

Problem 3

How much larger is 107³ than 97³?

Okay, lets begin

107³ – 97³ = 531,103.

Explanation

First, find the cube of 107³, which is 1,224,463.

Next, find the cube of 97³, which is 693,360.

Now, find the difference between them using the subtraction method. 1,224,463 – 693,360 = 531,103.

Therefore, 107³ is 531,103 larger than 97³.

Well explained 👍

Problem 4

If a cube with a side length of 107 cm is compared to a cube with a side length of 17 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 107 cm is 1,224,463 cm³.

Explanation

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

Cubing 107 means multiplying 107 by itself three times: 107 × 107 = 11,449, and then 11,449 × 107 = 1,224,463.

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

Therefore, the volume of the cube is 1,224,463 cm³.

Well explained 👍

Problem 5

Estimate the cube of 106.9 using the cube of 107.

Okay, lets begin

The cube of 106.9 is approximately 1,224,463.

Explanation

First, identify the cube of 107. The cube of 107 is 107³ = 1,224,463.

Since 106.9 is only a tiny bit less than 107, the cube of 106.9 will be almost the same as the cube of 107.

The cube of 106.9 is approximately 1,224,463 because the difference between 106.9 and 107 is very small.

So, we can approximate the value as 1,224,463.

Well explained 👍

FAQs on Cube of 107

1.What are the perfect cubes up to 107?

The perfect cubes up to 107 are 1, 8, 27, 64, and 125.

2.How do you calculate 107³?

To calculate 107³, use the multiplication method, 107 × 107 × 107, which equals 1,224,463.

3.What is the meaning of 107³?

107³ means 107 multiplied by itself three times or 107 × 107 × 107.

4.What is the cube root of 107?

5.Is 107 a perfect cube?

No, 107 is not a perfect cube because no integer multiplied by itself three times equals 107.

Important Glossaries for Cube of 107

  • 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.
  • Volume of a Cube: The amount of space enclosed within a cube, calculated as the side length raised to the third power (Side³).
  • Perfect Cube: A number that can be expressed as the cube of an integer.

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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.

Fun Fact

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