Cube of 680
2026-02-28 10:54 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 680.

Cube of 680

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 680 can be written as 680³, which is the exponential form. Or it can also be written in arithmetic form as, 680 × 680 × 680.

How to Calculate the Value of Cube of 680

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. 680³ = 680 × 680 × 680

Step 2: You get 314,432,000 as the answer. Hence, the cube of 680 is 314,432,000.

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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 680 into two parts, such as 600 and 80. Let a = 600 and b = 80, so a + b = 680

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

Step 3: Calculate each term

a³ = 600³

3a²b = 3 × 600² × 80

3ab² = 3 × 600 × 80²

b³ = 80³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(600 + 80)³ = 600³ + 3 × 600² × 80 + 3 × 600 × 80² + 80³

680³ = 216,000,000 + 86,400,000 + 23,040,000 + 512,000

680³ = 314,432,000

Step 5: Hence, the cube of 680 is 314,432,000.

Using a Calculator

To find the cube of 680 using a calculator, input the number 680 and use the cube function (if available) or multiply 680 × 680 × 680. This operation calculates the value of 680³, resulting in 314,432,000. 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 8 and 0

Step 3: If the calculator has a cube function, press it to calculate 680³.

Step 4: If there is no cube function on the calculator, simply multiply 680 three times manually.

Step 5: The calculator will display 314,432,000.

Tips and Tricks for the Cube of 680

  • 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 680

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 680?

Okay, lets begin

The cube of 680 is 314,432,000 and the cube root of 680 is approximately 8.79.

Explanation

First, let’s find the cube of 680.

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 680³ = 314,432,000

Next, we must find the cube root of 680 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 ∛680 ≈ 8.79

Hence the cube of 680 is 314,432,000 and the cube root of 680 is approximately 8.79.

Well explained 👍

Problem 2

If the side length of the cube is 680 cm, what is the volume?

Okay, lets begin

The volume is 314,432,000 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 680 for the side length: V = 680³ = 314,432,000 cm³.

Well explained 👍

Problem 3

How much larger is 680³ than 600³?

Okay, lets begin

680³ – 600³ = 98,432,000.

Explanation

First find the cube of 680³, that is 314,432,000

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

Now, find the difference between them using the subtraction method. 314,432,000 – 216,000,000 = 98,432,000

Therefore, the 680³ is 98,432,000 larger than 600³.

Well explained 👍

Problem 4

If a cube with a side length of 680 cm is compared to a cube with a side length of 80 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 680 cm is 314,432,000 cm³.

Explanation

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

Cubing 680 means multiplying 680 by itself three times: 680 × 680 = 462,400, and then 462,400 × 680 = 314,432,000.

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

Therefore, the volume of the cube is 314,432,000 cm³.

Well explained 👍

Problem 5

Estimate the cube 679.9 using the cube 680.

Okay, lets begin

The cube of 679.9 is approximately 314,432,000.

Explanation

First, identify the cube of 680, The cube of 680 is 680³ = 314,432,000.

Since 679.9 is only a tiny bit less than 680, the cube of 679.9 will be almost the same as the cube of 680.

The cube of 679.9 is approximately 314,432,000 because the difference between 679.9 and 680 is very small.

So, we can approximate the value as 314,432,000.

Well explained 👍

FAQs on Cube of 680

1.What are the perfect cubes up to 680?

The perfect cubes up to 680 include numbers like 1, 8, 27, 64, 125, 216, 343, and 512.

2.How do you calculate 680³?

To calculate 680³, use the multiplication method, 680 × 680 × 680, which equals 314,432,000.

3.What is the meaning of 680³?

680³ means 680 multiplied by itself three times, or 680 × 680 × 680.

4.What is the cube root of 680?

5.Is 680 a perfect cube?

No, 680 is not a perfect cube because no integer multiplied by itself three times equals 680.

Important Glossaries for Cube of 680

  • 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 to 8.
  • Volume of a Cube: The volume of a cube is found by cubing the side length, represented as Side³.
  • Cube Root: The cube root of a number is the value that, when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3.

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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.