Cube of 210
2026-02-28 01:46 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 210.

Cube of 210

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 210 can be written as 210³, which is the exponential form. Or it can also be written in arithmetic form as 210 × 210 × 210.

How to Calculate the Value of Cube of 210

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

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.

210³ = 210 × 210 × 210

Step 2: You get 9,261,000 as the answer.

Hence, the cube of 210 is 9,261,000.

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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 210 into two parts, as 200 and 10. Let a = 200 and b = 10, so a + b = 210

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

Step 3: Calculate each term a³ = 200³ , 3a²b = 3 × 200² × 10 , 3ab² = 3 × 200 × 10² , b³ = 10³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³

(200 + 10)³ = 200³ + 3 × 200² × 10 + 3 × 200 × 10² + 10³ 210³

= 8,000,000 + 1,200,000 + 60,000 + 1,000 210³ = 9,261,000

Step 5: Hence, the cube of 210 is 9,261,000.

Using a Calculator

To find the cube of 210 using a calculator, input the number 210 and use the cube function (if available) or multiply 210 × 210 × 210. This operation calculates the value of 210³, resulting in 9,261,000. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 2 followed by 1 and 0

Step 3: If the calculator has a cube function, press it to calculate 210³.

Step 4: If there is no cube function on the calculator, simply multiply 210 three times manually.

Step 5: The calculator will display 9,261,000.

Tips and Tricks for the Cube of 210

  • 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 210

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 210?

Okay, lets begin

The cube of 210 is 9,261,000 and the cube root of 210 is approximately 5.978.

Explanation

First, let’s find the cube of 210.

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

So, we get 210³ = 9,261,000.

Next, we must find the cube root of 210.

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

So, we get ∛210 ≈ 5.978.

Hence, the cube of 210 is 9,261,000 and the cube root of 210 is approximately 5.978.

Well explained 👍

Problem 2

If the side length of the cube is 210 cm, what is the volume?

Okay, lets begin

The volume is 9,261,000 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 210 for the side length: V = 210³ = 9,261,000 cm³.

Well explained 👍

Problem 3

How much larger is 210³ than 200³?

Okay, lets begin

210³ – 200³ = 1,261,000.

Explanation

First, find the cube of 210³, which is 9,261,000.

Next, find the cube of 200³, which is 8,000,000.

Now, find the difference between them using the subtraction method.

9,261,000 – 8,000,000 = 1,261,000.

Therefore, the 210³ is 1,261,000 larger than 200³.

Well explained 👍

Problem 4

If a cube with a side length of 210 cm is compared to a cube with a side length of 10 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 210 cm is 9,261,000 cm³.

Explanation

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

Cubing 210 means multiplying 210 by itself three times: 210 × 210 = 44,100, and then 44,100 × 210 = 9,261,000.

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

Therefore, the volume of the cube is 9,261,000 cm³.

Well explained 👍

Problem 5

Estimate the cube of 209.9 using the cube of 210.

Okay, lets begin

The cube of 209.9 is approximately 9,261,000.

Explanation

First, identify the cube of 210, the cube of 210 is 210³ = 9,261,000.

Since 209.9 is only a tiny bit less than 210, the cube of 209.9 will be almost the same as the cube of 210.

The cube of 209.9 is approximately 9,261,000 because the difference between 209.9 and 210 is very small.

So, we can approximate the value as 9,261,000.

Well explained 👍

FAQs on Cube of 210

1.What are the perfect cubes up to 210?

The perfect cubes up to 210 are 1, 8, 27, 64, and 125.

2.How do you calculate 210³?

To calculate 210³, use the multiplication method, 210 × 210 × 210, which equals 9,261,000.

3.What is the meaning of 210³?

210³ means 210 multiplied by itself three times, or 210 × 210 × 210.

4.What is the cube root of 210?

5.Is 210 a perfect cube?

No, 210 is not a perfect cube because no integer multiplied by itself three times equals 210.

Important Glossaries for Cube of 210

  • 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.
  • Volume of a Cube: The amount of space enclosed within a cube, calculated as the cube of its side length, or 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.