Cube of 668
2026-02-28 17:56 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 cubes of 668.

Cube of 668

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 668 can be written as 668³, which is the exponential form. Or it can also be written in arithmetic form as, 668 × 668 × 668.

How to Calculate the Value of Cube of 668

In order to check whether a number is a cube number or not, we can use the following three methods, such as the 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. 668³ = 668 × 668 × 668

Step 2: You get 298,941,632 as the answer. Hence, the cube of 668 is 298,941,632.

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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 668 into two parts, as 600 and 68. Let a = 600 and b = 68, so a + b = 668

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

Step 3: Calculate each term a³ = 600³ 3a²b = 3 × 600² × 68 3ab² = 3 × 600 × 68² b³ = 68³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(600 + 68)³ = 600³ + 3 × 600² × 68 + 3 × 600 × 68² + 68³

668³ = 216,000,000 + 73,440,000 + 8,294,400 + 314,432

668³ = 298,941,632

Step 5: Hence, the cube of 668 is 298,941,632.

Using a Calculator

To find the cube of 668 using a calculator, input the number 668 and use the cube function (if available) or multiply 668 × 668 × 668. This operation calculates the value of 668³, resulting in 298,941,632. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 6 followed by 6 and 8

Step 3: If the calculator has a cube function, press it to calculate 668³.

Step 4: If there is no cube function on the calculator, simply multiply 668 three times manually.

Step 5: The calculator will display 298,941,632.

Tips and Tricks for the Cube of 668

  • 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 668

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 668?

Okay, lets begin

The cube of 668 is 298,941,632 and the cube root of 668 is approximately 8.757.

Explanation

First, let’s find the cube of 668.

We know that the 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 668³ = 298,941,632

Next, we must find the cube root of 668 We know that the 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 ∛668 ≈ 8.757

Hence, the cube of 668 is 298,941,632 and the cube root of 668 is approximately 8.757.

Well explained 👍

Problem 2

If the side length of the cube is 668 cm, what is the volume?

Okay, lets begin

The volume is 298,941,632 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 668 for the side length: V = 668³ = 298,941,632 cm³.

Well explained 👍

Problem 3

How much larger is 668³ than 600³?

Okay, lets begin

668³ – 600³ = 82,941,632.

Explanation

First find the cube of 668³, which is 298,941,632

Next, find the cube of 600³, which is 216,000,000

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

298,941,632 – 216,000,000 = 82,941,632

Therefore, 668³ is 82,941,632 larger than 600³.

Well explained 👍

Problem 4

If a cube with a side length of 668 cm is compared to a cube with a side length of 68 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 668 cm is 298,941,632 cm³.

Explanation

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

Cubing 668 means multiplying 668 by itself three times: 668 × 668 = 446,224, and then 446,224 × 668 = 298,941,632.

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

Therefore, the volume of the cube is 298,941,632 cm³.

Well explained 👍

Problem 5

Estimate the cube of 668.1 using the cube of 668.

Okay, lets begin

The cube of 668.1 is approximately 298,941,632.

Explanation

First, identify the cube of 668, The cube of 668 is 668³ = 298,941,632.

Since 668.1 is only a tiny bit more than 668, the cube of 668.1 will be almost the same as the cube of 668.

The cube of 668.1 is approximately 298,941,632 because the difference between 668.1 and 668 is very small.

So, we can approximate the value as 298,941,632.

Well explained 👍

FAQs on Cube of 668

1.What are the perfect cubes up to 668?

The perfect cubes up to 668 are 1, 8, 27, 64, 125, 216, 343, 512.

2.How do you calculate 668³?

To calculate 668³, use the multiplication method, 668 × 668 × 668, which equals 298,941,632.

3.What is the meaning of 668³?

668³ means 668 multiplied by itself three times, or 668 × 668 × 668.

4.What is the cube root of 668?

5.Is 668 a perfect cube?

No, 668 is not a perfect cube because no integer multiplied by itself three times equals 668.

Important Glossaries for Cube of 668

  • 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 cube of an integer.
  • Cube Root: The value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2.

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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.