Cube of 728
2026-02-28 17:45 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 in comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 728.

Cube of 728

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 728 can be written as 728³, which is the exponential form. Or it can also be written in arithmetic form as, 728 × 728 × 728.

How to Calculate the Value of Cube of 728

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.

  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. 728³ = 728 × 728 × 728

Step 2: You get 385,800,832 as the answer. Hence, the cube of 728 is 385,800,832.

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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 728 into two parts. Let a = 700 and b = 28, so a + b = 728

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

Step 3: Calculate each term

a³ = 700³

3a²b = 3 × 700² × 28

3ab² = 3 × 700 × 28²

b³ = 28³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(700 + 28)³ = 700³ + 3 × 700² × 28 + 3 × 700 × 28² + 28³

728³ = 343,000,000 + 41,160,000 + 16,464,000 + 21,952

728³ = 385,800,832

Step 5: Hence, the cube of 728 is 385,800,832.

Using a Calculator

To find the cube of 728 using a calculator, input the number 728 and use the cube function (if available) or multiply 728 × 728 × 728. This operation calculates the value of 728³, resulting in 385,800,832. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Enter 728

Step 3: If the calculator has a cube function, press it to calculate 728³.

Step 4: If there is no cube function on the calculator, simply multiply 728 three times manually.

Step 5: The calculator will display 385,800,832.

Tips and Tricks for the Cube of 728

  • 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 728

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 728?

Okay, lets begin

The cube of 728 is 385,800,832 and the cube root of 728 is approximately 8.945.

Explanation

First, let’s find the cube of 728.

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 728³ = 385,800,832

Next, we must find the cube root of 728 We know that cube root of a number ‘x’, such that ∛x = y Where ‘x’ is the given number, and y is the cube root value of the number

So, we get ∛728 ≈ 8.945

Hence the cube of 728 is 385,800,832 and the cube root of 728 is approximately 8.945.

Well explained 👍

Problem 2

If the side length of the cube is 728 cm, what is the volume?

Okay, lets begin

The volume is 385,800,832 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 728 for the side length: V = 728³ = 385,800,832 cm³.

Well explained 👍

Problem 3

How much larger is 728³ than 530³?

Okay, lets begin

728³ – 530³ = 286,678,672.

Explanation

First, find the cube of 728, which is 385,800,832

Next, find the cube of 530, which is 99,122,160

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

385,800,832 – 99,122,160 = 286,678,672

Therefore, the 728³ is 286,678,672 larger than 530³.

Well explained 👍

Problem 4

If a cube with a side length of 728 cm is compared to a cube with a side length of 128 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 728 cm is 385,800,832 cm³.

Explanation

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

Cubing 728 means multiplying 728 by itself three times: 728 × 728 = 529,984, and then 529,984 × 728 = 385,800,832.

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

Therefore, the volume of the cube is 385,800,832 cm³.

Well explained 👍

Problem 5

Estimate the cube of 727 using the cube of 728.

Okay, lets begin

The cube of 727 is approximately 384,261,273.

Explanation

First, identify the cube of 728, The cube of 728 is 728³ = 385,800,832.

Since 727 is only a tiny bit less than 728, the cube of 727 will be almost the same as the cube of 728.

The cube of 727 is slightly less than the cube of 728 due to the small difference.

Well explained 👍

FAQs on Cube of 728

1.What are the perfect cubes up to 728?

The perfect cubes up to 728 are 1, 8, 27, 64, 125, 216, 343, 512.

2.How do you calculate 728³?

To calculate 728³, use the multiplication method, 728 × 728 × 728, which equals 385,800,832.

3.What is the meaning of 728³?

728³ means 728 is multiplied by itself three times, or 728 × 728 × 728.

4.What is the cube root of 728?

5.Is 728 a perfect cube?

No, 728 is not a perfect cube because no integer multiplied by itself three times equals 728.

Important Glossaries for Cube of 728

  • Binomial Formula: 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: 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 cube of an integer.
  • Volume of a Cube: The space inside a cube, calculated as the side length cubed (S³).

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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.