Cube of 7
2026-02-28 08:56 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 7.

Cube of 7

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 7 can be written as 7³, which is the exponential form. Or it can also be written in arithmetic form as 7 × 7 × 7.

How to Calculate the Value of Cube of 7

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

  1. By Multiplication Method
  2. Using a Formula
  3. 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. 7³ = 7 × 7 × 7

Step 2: You get 343 as the answer. Hence, the cube of 7 is 343.

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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 7 into two parts, as 4 and 3. Let a = 4 and b = 3, so a + b = 7

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

Step 3: Calculate each term

a³ = 4³

3a²b = 3 × 4² × 3

3ab² = 3 × 4 × 3²

b³ = 3³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(4 + 3)³ = 4³ + 3 × 4² × 3 + 3 × 4 × 3² + 3³

7³ = 64 + 144 + 108 + 27

7³ = 343

Step 5: Hence, the cube of 7 is 343.

Using a Calculator

To find the cube of 7 using a calculator, input the number 7 and use the cube function (if available) or multiply 7 × 7 × 7. This operation calculates the value of 7³, resulting in 343. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 7

Step 3: If the calculator has a cube function, press it to calculate 7³.

Step 4: If there is no cube function on the calculator, simply multiply 7 three times manually.

Step 5: The calculator will display 343.

Tips and Tricks for the Cube of 7

  • 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 7

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 7?

Okay, lets begin

The cube of 7 is 343 and the cube root of 7 is approximately 1.913.

Explanation

First, let’s find the cube of 7.

We know that the cube of a number is x³ = y Where x is the given number, and y is the cubed value of that number

So, we get 7³ = 343

Next, we must find the cube root of 7 We know that the cube root of a number ‘x’ is ∛x = y Where x is the given number, and y is the cube root value of the number

So, we get ∛7 ≈ 1.913

Hence, the cube of 7 is 343 and the cube root of 7 is approximately 1.913.

Well explained 👍

Problem 2

If the side length of the cube is 7 cm, what is the volume?

Okay, lets begin

The volume is 343 cm³.

Explanation

Use the volume formula for a cube V = Side³. Substitute 7 for the side length: V = 7³ = 343 cm³.

Well explained 👍

Problem 3

How much larger is 7³ than 5³?

Okay, lets begin

7³ – 5³ = 218.

Explanation

First, find the cube of 7³, which is 343

Next, find the cube of 5³, which is 125

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

343 – 125 = 218

Therefore, 7³ is 218 larger than 5³.

Well explained 👍

Problem 4

If a cube with a side length of 7 cm is compared to a cube with a side length of 3 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 7 cm is 343 cm³.

Explanation

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

Cubing 7 means multiplying 7 by itself three times: 7 × 7 = 49, and then 49 × 7 = 343.

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

Therefore, the volume of the cube is 343 cm³.

Well explained 👍

Problem 5

Estimate the cube of 6.9 using the cube of 7.

Okay, lets begin

The cube of 6.9 is approximately 343.

Explanation

First, identify the cube of 7, The cube of 7 is 7³ = 343.

Since 6.9 is only a tiny bit less than 7, the cube of 6.9 will be almost the same as the cube of 7.

The cube of 6.9 is approximately 343 because the difference between 6.9 and 7 is very small.

So, we can approximate the value as 343.

Well explained 👍

FAQs on Cube of 7

1.What are the perfect cubes up to 7?

The perfect cubes up to 7 are 1 and 8.

2.How do you calculate 7³?

To calculate 7³, use the multiplication method, 7 × 7 × 7, which equals 343.

3.What is the meaning of 7³?

7³ means 7 multiplied by itself three times, or 7 × 7 × 7.

4.What is the cube root of 7?

5.Is 7 a perfect cube?

No, 7 is not a perfect cube because no integer multiplied by itself three times equals 7.

Important Glossaries for Cube of 7

  • 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.
  • Perfect Cube: A number that can be expressed as the product of three identical integers. For example, 27 is a perfect cube because 3 × 3 × 3 = 27.
  • Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number. It is represented by the symbol ∛.

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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.