Cube of 1
2026-02-28 09:01 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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 1.

Cube of 1

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 1 can be written as 1³, which is the exponential form.

Or it can also be written in arithmetic form as, 1 × 1 × 1.

How to Calculate the Value of Cube of 1

In order 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 numbers 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. 1³ = 1 × 1 × 1

Step 2: You get 1 as the answer.

Hence, the cube of 1 is 1.

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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 1 into two parts, as 0 and 1. Let a = 0 and b = 1, so a + b = 1

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

Step 3: Calculate each term a³ = 0³ 3a²b = 3 × 0² × 1 3ab² = 3 × 0 × 1² b³ = 1³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (0 + 1)³ = 0³ + 3 × 0² × 1 + 3 × 0 × 1² + 1³ 1³ = 0 + 0 + 0 + 1 1³ = 1

Step 5: Hence, the cube of 1 is 1.

Using a Calculator

To find the cube of 1 using a calculator, input the number 1 and use the cube function (if available) or multiply 1 × 1 × 1. This operation calculates the value of 1³, resulting in 1. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 1

Step 3: If the calculator has a cube function, press it to calculate 1³.

Step 4: If there is no cube function on the calculator, simply multiply 1 three times manually.
 

Step 5: The calculator will display 1.

Tips and Tricks for the Cube of 1

  • 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 1

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 1?

Okay, lets begin

The cube of 1 is 1 and the cube root of 1 is 1.

Explanation

First, let’s find the cube of 1.

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 1³ = 1 Next, we must find the cube root of 1

We know that the cube root of a number ‘x’, 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√1 = 1 Hence the cube of 1 is 1 and the cube root of 1 is 1.

Well explained 👍

Problem 2

If the side length of the cube is 1 cm, what is the volume?

Okay, lets begin

The volume is 1 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 1 for the side length: V = 1³ = 1 cm³.

Well explained 👍

Problem 3

How much larger is 1³ than 0³?

Okay, lets begin

1³ - 0³ = 1.

Explanation

First, find the cube of 1³, that is 1

Next, find the cube of 0³, which is 0

Now, find the difference between them using the subtraction method. 1 - 0 = 1

Therefore, 1³ is 1 larger than 0³.

Well explained 👍

Problem 4

If a cube with a side length of 1 cm is compared to a cube with a side length of 0.5 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 1 cm is 1 cm³

Explanation

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

Cubing 1 means multiplying 1 by itself three times: 1 × 1 = 1, and then 1 × 1 = 1.

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 cm³.

Well explained 👍

Problem 5

Estimate the cube 0.9 using the cube 1.

Okay, lets begin

The cube of 0.9 is approximately 0.729.

Explanation

First, identify the cube of 1, The cube of 1 is 1³ = 1.

Since 0.9 is less than 1, the cube of 0.9 will be less than the cube of 1.

The cube of 0.9 is approximately 0.729 because the difference between 0.9 and 1 affects the cubed result.

Well explained 👍

FAQs on Cube of 1

1.What are the perfect cubes up to 1?

The perfect cube up to 1 is 1.

2.How do you calculate 1³?

To calculate 1³, use the multiplication method, 1 × 1 × 1, which equals 1.

3.What is the meaning of 1³?

1³ means 1 multiplied by itself three times, or 1 × 1 × 1.

4.What is the cube root of 1?

5.Is 1 a perfect cube?

Yes, 1 is a perfect cube because 1 multiplied by itself three times equals 1.

Important Glossaries for Cube of 1

  • 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, equaling 8.
  • Perfect Cube: A number that can be expressed as the cube of an integer.
  • Volume of a Cube: The amount of space enclosed within a cube, calculated by cubing the side length (Side³).

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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.