Cube of 213
2026-02-28 13:19 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 213.

Cube of 213

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 213 can be written as \(213^3\), which is the exponential form. Or it can also be written in arithmetic form as, \(213 \times 213 \times 213\).

How to Calculate the Value of Cube of 213

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 (\(a^3\)), 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 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. \(213^3 = 213 \times 213 \times 213\) Step 2: You get 9,665,157 as the answer. Hence, the cube of 213 is 9,665,157.

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Using a Formula (\(a^3\))

The formula (\(a + b\))^3 is a binomial formula for finding the cube of a number. The formula is expanded as \(a^3 + 3a^2b + 3ab^2 + b^3\). Step 1: Split the number 213 into two parts, as 200 and 13. Let \(a = 200\) and \(b = 13\), so \(a + b = 213\). Step 2: Now, apply the formula \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\). Step 3: Calculate each term \(a^3= 200^3\) \(3a^2b = 3 \times 200^2 \times 13\) \(3ab^2 = 3 \times 200 \times 13^2\) \(b^3 = 13^3\) Step 4: Add all the terms together: \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) \((200 + 13)^3 = 200^3 + 3 \times 200^2 \times 13 + 3 \times 200 \times 13^2 + 13^3\) \(213^3 = 8,000,000 + 1,560,000 + 101,400 + 2,197\) \(213^3 = 9,665,157\) Step 5: Hence, the cube of 213 is 9,665,157.

Using a Calculator

To find the cube of 213 using a calculator, input the number 213 and use the cube function (if available) or multiply \(213 \times 213 \times 213\). This operation calculates the value of \(213^3\), resulting in 9,665,157. 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 then 3. Step 3: If the calculator has a cube function, press it to calculate \(213^3\). Step 4: If there is no cube function on the calculator, simply multiply 213 three times manually. Step 5: The calculator will display 9,665,157.

Tips and Tricks for the Cube of 213

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 213

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 213?

Okay, lets begin

The cube of 213 is 9,665,157 and the cube root of 213 is approximately 5.996.

Explanation

First, let’s find the cube of 213. We know that the cube of a number, such that \(x^3 = y\) Where \(x\) is the given number, and \(y\) is the cubed value of that number. So, we get \(213^3 = 9,665,157\). Next, we must find the cube root of 213. We know that the cube root of a number \(x\), such that \(\sqrt[3]{x} = y\). Where \(x\) is the given number, and \(y\) is the cube root value of the number. So, we get \(\sqrt[3]{213} \approx 5.996\). Hence, the cube of 213 is 9,665,157 and the cube root of 213 is approximately 5.996.

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Problem 2

If the side length of the cube is 213 cm, what is the volume?

Okay, lets begin

The volume is 9,665,157 cm\(^3\).

Explanation

Use the volume formula for a cube \(V = \text{Side}^3\). Substitute 213 for the side length: \(V = 213^3 = 9,665,157\) cm\(^3\).

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Problem 3

How much larger is \(213^3\) than \(200^3\)?

Okay, lets begin

\(213^3 - 200^3 = 1,665,157\).

Explanation

First, find the cube of 213, which is 9,665,157. Next, find the cube of 200, which is 8,000,000. Now, find the difference between them using the subtraction method. 9,665,157 - 8,000,000 = 1,665,157. Therefore, \(213^3\) is 1,665,157 larger than \(200^3\).

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Problem 4

If a cube with a side length of 213 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 213 cm is 9,665,157 cm\(^3\).

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing 213 means multiplying 213 by itself three times: 213 \times 213 = 45,369, and then 45,369 \times 213 = 9,665,157. The unit of volume is cubic centimeters (cm\(^3\)), because we are calculating the space inside the cube. Therefore, the volume of the cube is 9,665,157 cm\(^3\).

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Problem 5

Estimate the cube of 212.9 using the cube of 213.

Okay, lets begin

The cube of 212.9 is approximately 9,665,157.

Explanation

First, identify the cube of 213. The cube of 213 is \(213^3 = 9,665,157\). Since 212.9 is only a tiny bit less than 213, the cube of 212.9 will be almost the same as the cube of 213. The cube of 212.9 is approximately 9,665,157 because the difference between 212.9 and 213 is very small. So, we can approximate the value as 9,665,157.

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FAQs on Cube of 213

1.What are the perfect cubes up to 213?

The perfect cubes up to 213 are 1, 8, 27, 64, 125, and 216.

2.How do you calculate \(213^3\)?

To calculate \(213^3\), use the multiplication method, \(213 \times 213 \times 213\), which equals 9,665,157.

3.What is the meaning of \(213^3\)?

\(213^3\) means 213 multiplied by itself three times, or \(213 \times 213 \times 213\).

4.What is the cube root of 213?

5.Is 213 a perfect cube?

No, 213 is not a perfect cube because no integer multiplied by itself three times equals 213.

Important Glossaries for Cube of 213

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, \(2^3\) represents \(2 \times 2 \times 2\) equals 8. Volume of a Cube: The amount of space occupied by a cube, calculated as the cube of its side length. 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.

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