Cube of 137
2026-02-28 12:44 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 sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 137.

Cube of 137

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 137 can be written as 137³, which is the exponential form.

Or it can also be written in arithmetic form as 137 × 137 × 137.

How to Calculate the Value of Cube of 137

In order to check whether a number is a cube number or not, we can use the following three methods: multiplication method, a factor formula (a³), or by using a calculator. These three methods will help 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. 137³ = 137 × 137 × 137

Step 2: You get 2,573,737 as the answer. Hence, the cube of 137 is 2,573,737.

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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 137 into two parts, as a and b. Let a = 130 and b = 7, so a + b = 137

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

Step 3: Calculate each term a³ = 130³ 3a²b = 3 × 130² × 7 3ab² = 3 × 130 × 7² b³ = 7³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (130 + 7)³= 130³ + 3 × 130² × 7 + 3 × 130 × 7² + 7³ 137³ = 2,197,000 + 355,300 + 63,700 + 343 137³ = 2,573,737

Step 5: Hence, the cube of 137 is 2,573,737.

Using a Calculator

To find the cube of 137 using a calculator, input the number 137 and use the cube function (if available) or multiply 137 × 137 × 137. This operation calculates the value of 137³, resulting in 2,573,737. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 1 followed by 3 and 7

Step 3: If the calculator has a cube function, press it to calculate 137³.

Step 4: If there is no cube function on the calculator, simply multiply 137 three times manually.

Step 5: The calculator will display 2,573,737.

Tips and Tricks for the Cube of 137

  • 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 137

There are some typical errors that might occur during the process of cubing a number. Let us take a look at five of the major mistakes that might happen:

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Problem 1

What is the cube and cube root of 137?

Okay, lets begin

The cube of 137 is 2,573,737 and the cube root of 137 is approximately 5.152.

Explanation

First, let’s find the cube of 137.

We know that 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 137³ = 2,573,737 Next, we must find the cube root of 137

We know that cube root of a number ‘x’, such that ³√x = y

Where ‘x’ is the given number, and y is the cube root value of the number

So, we get ³√137 ≈ 5.152

Hence the cube of 137 is 2,573,737 and the cube root of 137 is approximately 5.152.

Well explained 👍

Problem 2

If the side length of the cube is 137 cm, what is the volume?

Okay, lets begin

The volume is 2,573,737 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 137 for the side length: V = 137³ = 2,573,737 cm³.

Well explained 👍

Problem 3

How much larger is 137³ than 130³?

Okay, lets begin

137³ – 130³ = 376,737.

Explanation

First find the cube of 137³, that is 2,573,737

Next, find the cube of 130³, which is 2,197,000

Now, find the difference between them using the subtraction method. 2,573,737 – 2,197,000 = 376,737

Therefore, 137³ is 376,737 larger than 130³.

Well explained 👍

Problem 4

If a cube with a side length of 137 cm is compared to a cube with a side length of 7 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 137 cm is 2,573,737 cm³.

Explanation

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

Cubing 137 means multiplying 137 by itself three times: 137 × 137 = 18,769, and then 18,769 × 137 = 2,573,737.

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

Therefore, the volume of the cube is 2,573,737 cm³.

Well explained 👍

Problem 5

Estimate the cube 136.9 using the cube 137.

Okay, lets begin

The cube of 136.9 is approximately 2,573,737.

Explanation

First, identify the cube of 137,

The cube of 137 is 137³ = 2,573,737.

Since 136.9 is only a tiny bit less than 137, the cube of 136.9 will be almost the same as the cube of 137.

The cube of 136.9 is approximately 2,573,737 because the difference between 136.9 and 137 is very small.

So, we can approximate the value as 2,573,737.

Well explained 👍

FAQs on Cube of 137

1.What are the perfect cubes up to 137?

The perfect cubes up to 137 are 1, 8, 27, 64, and 125.

2.How do you calculate 137³?

To calculate 137³, use the multiplication method, 137 × 137 × 137, which equals 2,573,737.

3.What is the meaning of 137³?

137³ means 137 multiplied by itself three times, or 137 × 137 × 137.

4.What is the cube root of 137?

5.Is 137 a perfect cube?

No, 137 is not a perfect cube because no integer multiplied by itself three times equals 137.

Important Glossaries for Cube of 137

  • 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.
     
  • Perfect Cube: A number that can be expressed as the cube of an integer. For instance, 8 is a perfect cube because it equals 2³.
     
  • Volume of a Cube: The amount of space inside a cube, calculated using the formula V = side³, where 'side' is the length of one side of the cube.

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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.