Cube of 400
2026-02-28 12:59 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 cubes of 400.

Cube of 400

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 400 can be written as 400³, which is the exponential form.

Or it can also be written in arithmetic form as 400 × 400 × 400.

How to Calculate the Value of Cube of 400

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 (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. 400³ = 400 × 400 × 400

Step 2: You get 64,000,000 as the answer. Hence, the cube of 400 is 64,000,000.

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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 400 into two parts. Let a = 300 and b = 100, so a + b = 400

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

Step 3: Calculate each term a³ = 300³ 3a²b = 3 × 300² × 100 3ab² = 3 × 300 × 100² b³ = 100³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (300 + 100)³ = 300³ + 3 × 300² × 100 + 3 × 300 × 100² + 100³ 400³ = 27,000,000 + 27,000,000 + 9,000,000 + 1,000,000 400³ = 64,000,000

Step 5: Hence, the cube of 400 is 64,000,000.

Using a Calculator

To find the cube of 400 using a calculator, input the number 400 and use the cube function (if available) or multiply 400 × 400 × 400. This operation calculates the value of 400³, resulting in 64,000,000. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 4 followed by 0, 0

Step 3: If the calculator has a cube function, press it to calculate 400³.

Step 4: If there is no cube function on the calculator, simply multiply 400 three times manually.

Step 5: The calculator will display 64,000,000.

Tips and Tricks for the Cube of 400

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 400

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 400?

Okay, lets begin

The cube of 400 is 64,000,000 and the cube root of 400 is approximately 7.368.

Explanation

First, let’s find the cube of 400.

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 400³ = 64,000,000 Next, we must find the cube root of 400

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 ∛400 ≈ 7.368

Hence the cube of 400 is 64,000,000 and the cube root of 400 is approximately 7.368.

Well explained 👍

Problem 2

If the side length of the cube is 400 cm, what is the volume?

Okay, lets begin

The volume is 64,000,000 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 400 for the side length: V = 400³ = 64,000,000 cm³.

Well explained 👍

Problem 3

How much larger is 400³ than 300³?

Okay, lets begin

400³ – 300³ = 37,000,000.

Explanation

First find the cube of 400³, that is 64,000,000

Next, find the cube of 300³, which is 27,000,000

Now, find the difference between them using the subtraction method. 64,000,000 – 27,000,000 = 37,000,000

Therefore, the 400³ is 37,000,000 larger than 300³.

Well explained 👍

Problem 4

If a cube with a side length of 400 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 400 cm is 64,000,000 cm³.

Explanation

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

Cubing 400 means multiplying 400 by itself three times: 400 × 400 = 160,000, and then 160,000 × 400 = 64,000,000.

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

Therefore, the volume of the cube is 64,000,000 cm³.

Well explained 👍

Problem 5

Estimate the cube of 399.9 using the cube of 400.

Okay, lets begin

The cube of 399.9 is approximately 64,000,000.

Explanation

First, identify the cube of 400, The cube of 400 is 400³ = 64,000,000.

Since 399.9 is only a tiny bit less than 400, the cube of 399.9 will be almost the same as the cube of 400.

The cube of 399.9 is approximately 64,000,000 because the difference between 399.9 and 400 is very small.

So, we can approximate the value as 64,000,000.

Well explained 👍

FAQs on Cube of 400

1.What are the perfect cubes up to 400?

The perfect cubes up to 400 are 1, 8, 27, 64, 125, 216, and 343.

2.How do you calculate 400³?

To calculate 400³, use the multiplication method, 400 × 400 × 400, which equals 64,000,000.

3.What is the meaning of 400³?

400³ means 400 multiplied by itself three times, or 400 × 400 × 400.

4.What is the cube root of 400?

5.Is 400 a perfect cube?

No, 400 is not a perfect cube because no integer multiplied by itself three times equals 400.

Important Glossaries for Cube of 400

  • 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: A value that, when multiplied by itself three times, gives the original number. For example, the cube root of 64 is 4, because 4 × 4 × 4 equals 64.

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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.