Cube of 421
2026-02-28 17:14 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 the sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 421.

Cube of 421

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 421 can be written as 421³, which is the exponential form.

Or it can also be written in arithmetic form as 421 × 421 × 421.

How to Calculate the Value of Cube of 421

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 numbers faster and easier without feeling confused or stuck while evaluating the answers. 

  • By Multiplication Method 
     
  • Using a Formula 
     
  • 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. 421³ = 421 × 421 × 421

Step 2: You get 74,792,761 as the answer. Hence, the cube of 421 is 74,792,761.

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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 421 into two parts. Let a = 420 and b = 1, so a + b = 421

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

Step 3: Calculate each term: a³ = 420³ 3a²b = 3 × 420² × 1 3ab² = 3 × 420 × 1² b³ = 1³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (420 + 1)³ = 420³ + 3 × 420² × 1 + 3 × 420 × 1² + 1³ 421³ = 74,088,000 + 529,200 + 1,260 + 1 421³ = 74,792,761

Step 5: Hence, the cube of 421 is 74,792,761.

Using a Calculator

To find the cube of 421 using a calculator, input the number 421 and use the cube function (if available) or multiply 421 × 421 × 421. This operation calculates the value of 421³, resulting in 74,792,761. 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 2, then 1.

Step 3: If the calculator has a cube function, press it to calculate 421³.

Step 4: If there is no cube function on the calculator, simply multiply 421 three times manually.

Step 5: The calculator will display 74,792,761.

Tips and Tricks for the Cube of 421

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 421

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 421?

Okay, lets begin

The cube of 421 is 74,792,761 and the cube root of 421 is approximately 7.488.

Explanation

First, let’s find the cube of 421.

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 421³ = 74,792,761. Next, we must find the cube root of 421.

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 ∛421 ≈ 7.488.

Hence, the cube of 421 is 74,792,761 and the cube root of 421 is approximately 7.488.

Well explained 👍

Problem 2

If the side length of the cube is 421 cm, what is the volume?

Okay, lets begin

The volume is 74,792,761 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 421 for the side length: V = 421³ = 74,792,761 cm³.

Well explained 👍

Problem 3

How much larger is 421³ than 411³?

Okay, lets begin

421³ – 411³ = 9,487,761.

Explanation

First, find the cube of 421, which is 74,792,761.

Next, find the cube of 411, which is 65,305,000.

Now, find the difference between them using the subtraction method. 74,792,761 – 65,305,000 = 9,487,761.

Therefore, 421³ is 9,487,761 larger than 411³.

Well explained 👍

Problem 4

If a cube with a side length of 421 cm is compared to a cube with a side length of 21 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 421 cm is 74,792,761 cm³.

Explanation

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

Cubing 421 means multiplying 421 by itself three times: 421 × 421 = 177,241, and then 177,241 × 421 = 74,792,761.

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

Therefore, the volume of the cube is 74,792,761 cm³.

Well explained 👍

Problem 5

Estimate the cube of 420.1 using the cube of 421.

Okay, lets begin

The cube of 420.1 is approximately 74,792,761.

Explanation

First, identify the cube of 421, The cube of 421 is 421³ = 74,792,761.

Since 420.1 is only a tiny bit less than 421, the cube of 420.1 will be almost the same as the cube of 421.

The cube of 420.1 is approximately 74,792,761 because the difference between 420.1 and 421 is very small.

So, we can approximate the value as 74,792,761.

Well explained 👍

FAQs on Cube of 421

1.What are the perfect cubes up to 421?

The perfect cubes up to 421 are 1, 8, 27, 64, 125, 216, and 343.

2.How do you calculate 421³?

To calculate 421³, use the multiplication method, 421 × 421 × 421, which equals 74,792,761.

3.What is the meaning of 421³?

421³ means 421 multiplied by itself three times, or 421 × 421 × 421.

4.What is the cube root of 421?

5.Is 421 a perfect cube?

No, 421 is not a perfect cube because no integer multiplied by itself three times equals 421.

Important Glossaries for Cube of 421

  • 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, which equals 8.
  • Volume of a Cube: The amount of space enclosed within a cube, calculated as 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.