Cube of 31
2026-02-28 23:57 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-31

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Last updated on August 5, 2025

When a number is multiplied by itself thrice, the result is its cube. Cubes are commonly used in furniture design, architecture, urban planning, etc. In this topic, let us examine the property of the cube of 31.

What is the Cube of 31?

A cube of a number is the product of the same number when it is multiplied by itself thrice. Cubes are also known as perfect cubes. The cube of positive numbers is positive and the cube of negative numbers is negative. This is because if we multiply a negative number three times, it results in a negative value. 

The cubes of positive numbers are positive. The cube of negative numbers is negative because when we multiply a negative number three times it gives a negative number as the result.

  • Cube of 31: 313= 29791
  • Cube of 31 in Exponential form: 313
  • Cube of 31 in Arithmetic form: 31 × 31 × 31

How to Calculate the Value of Cube of 31?

To calculate the cube of a number, you can multiply the number by itself three times. To find the cube of 31 we use the following methods:

  • By Multiplication Method
  • Using a Formula (a3)
  • Using a Calculator

By Multiplication Method

This method includes the multiplication of the number by itself thrice to find its cube.


Use these steps to determine the cube of a number:


Step 1: First write the number.

31

Step 2: Multiply 31 by itself to get 312.

31 x 31 = 961

Step 3: Multiply 312 with 31 to get 313

 961 x 31 = 29791.

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Using a formula (a cube)

This formula is used to find the cube of a number by expanding the expression   (a+b)3= a3 + 3a2b + 3ab2 + b3

Step 1: Cubing a number means, multiplying the number by itself three times

Here a = 31 so:
 31 × 31 × 31 = (313)


Step 2: Break the number into two parts (a and b) : 
 313= (30 + 1)3

Step 3: Apply the formula:
(a + b)3= a3 + 3a2b + 3ab2 + b3
 (30+1)3= 303+ 3 (30)2(1) + 3 (30)(1)2 + 13 

Step4: Now we calculate each part:
303= 30 x 30 x 30 = 27000
3(30)2(1) = 3 x (30 x 30) x 1 = 3 x 900 = 2700
 3(30)(1)2= 3 x 30 x 1 = 90
  13= 1

Step5: Add the terms:
27000 + 2700 + 90 + 1 = 29791

Step6: Final result:
313= 29791

By using Calculator

To calculate the cube of 31 using a calculator, you can follow the steps mentioned below to find the answer.

  Step 1: Enter the number 31 in the calculator.

Step 2: Press the cube button ( x3) if available, or you can manually type 31 x 31 x 31.

Step 3: Press the enter button. The calculator will give you the result as 29791.

The cube of 31 is 29791.
 

Tips and Tricks for the Cube of 31

Kids can learn cube of a number quickly by using the following tips and tricks.

  • The cube of odd numbers will always be an odd number.
  • The sum of successive odd numbers can be used to describe perfect cube numbers.
  • The cube of a number denotes the volume of a cube.

Common Mistakes to Avoid When Calculating the Cube of 31

Calculating the cube of a number is an important topic, but students face challenges. Here are a few common mistakes to look out for when cubing a number. 

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Problem 1

Find the difference between 31³and 30³?

Okay, lets begin

313= 29791


303= 27000


 313-   303= 29791 - 27000 = 2791.

Explanation

The cube of 31 is 29791 and the cube of 30 is 27000 the difference between them is 2791.

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Problem 2

A cube of 31cm weighs 2 grams per cubic cm. What is the total weight of the cube?

Okay, lets begin

Volume(v)  =  313= 29791


Weight = 29791 × 2 


The total weight is, 59582g

Explanation

The volume of a cube whose side is 31cm is 29791 cm3. The total weight of the cube is 59582 grams.

Well explained 👍

Problem 3

A cube has a side length of 31cm. What is its volume?

Okay, lets begin

Volume = side x side x side


Volume = 31 x 31 x 31 = 29791

Explanation

The length of each side of a cube is 31. The volume of the cube is side3. The final result is 29791 cm3.

Well explained 👍

Problem 4

Simplify (31³)².

Okay, lets begin

Using the property (am)n = am.n


(313)2= 313 . 2 =  316.

Explanation

The rule of exponent states that when we are raising a power to another, we can multiply the exponents. The final answer is  316.

Well explained 👍

Problem 5

Simplify (31³+ 2000)

Okay, lets begin

313= 29791 


29791 + 2000 = 31791

Explanation

The cube of 31 is 29,791. Add 2000 the final result is 31,791.

Well explained 👍

FAQs on Cube of 31

1.What is the cube of 31?

2.What is the cube root of 31?

The cube root of 31 is 3.141. This is an approximate value as 31 is not a perfect cube and cube root of 31 is an irrational number.

3.Is 32 a perfect cube?

No, 32 not a perfect cube.

4.How to find the cube of 31?

A cube of 31 can be found by using the multiplication method, cube number formula, or by using a calculator for faster results 

5.What is the cube formula?

The formula of cube is   (a + b)3= a3 + 3a2b + 3ab2 + b3

Important glossaries for Cube of 31

Exponent: It is a way of expressing a number as a power of another. For example, 23, here 2 is the base and 3 is the exponent.

Volume: Volume of an object is the space occupied by a three-dimensional object. For example, the volume of a cube, cuboid. 


Cube Root: The cube root is an inverse operation of cubing a number. For example, ∛125 is 5.

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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.