Cube of 687
2026-02-28 17:17 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 useful when comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 687.

Cube of 687

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 687 can be written as 687³, which is the exponential form. Or it can also be written in arithmetic form as, 687 × 687 × 687.

How to Calculate the Value of Cube of 687

To check whether a number is a cube number or not, we can use the following three methods: the multiplication method, a factor formula (a³), or by using a calculator. These methods help in cubing numbers faster and easier without confusion or errors. -

  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. 687³ = 687 × 687 × 687

Step 2: You get 324,631,023 as the answer. Hence, the cube of 687 is 324,631,023.

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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 687 into two parts, as 600 and 87. Let a = 600 and b = 87, so a + b = 687

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

Step 3: Calculate each term

a³ = 600³

3a²b = 3 × 600² × 87

3ab² = 3 × 600 × 87²

b³ = 87³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(600 + 87)³ = 600³ + 3 × 600² × 87 + 3 × 600 × 87² + 87³

687³ = 216,000,000 + 93,960,000 + 13,658,400 + 658,503

687³ = 324,631,023

Step 5: Hence, the cube of 687 is 324,631,023.

Using a Calculator

To find the cube of 687 using a calculator, input the number 687 and use the cube function (if available) or multiply 687 × 687 × 687. This operation calculates the value of 687³, resulting in 324,631,023. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Enter 687 into the calculator.

Step 3: If the calculator has a cube function, press it to calculate 687³.

Step 4: If there is no cube function on the calculator, simply multiply 687 three times manually.

Step 5: The calculator will display 324,631,023.

Tips and Tricks for the Cube of 687

  • 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 687

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 occur:

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Problem 1

What is the cube and cube root of 687?

Okay, lets begin

The cube of 687 is 324,631,023 and the cube root of 687 is approximately 8.848.

Explanation

First, let’s find the cube of 687.

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 687³ = 324,631,023.

Next, we must find the cube root of 687. 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 ∛687 ≈ 8.848.

Hence the cube of 687 is 324,631,023 and the cube root of 687 is approximately 8.848.

Well explained 👍

Problem 2

If the side length of the cube is 687 cm, what is the volume?

Okay, lets begin

The volume is 324,631,023 cm³.

Explanation

Use the volume formula for a cube V = Side³. Substitute 687 for the side length: V = 687³ = 324,631,023 cm³.

Well explained 👍

Problem 3

How much larger is 687³ than 600³?

Okay, lets begin

687³ – 600³ = 108,631,023.

Explanation

First, find the cube of 687, which is 324,631,023.

Next, find the cube of 600, which is 216,000,000.

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

324,631,023 – 216,000,000 = 108,631,023.

Therefore, 687³ is 108,631,023 larger than 600³.

Well explained 👍

Problem 4

If a cube with a side length of 687 cm is compared to a cube with a side length of 100 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 687 cm is 324,631,023 cm³.

Explanation

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

Cubing 687 means multiplying 687 by itself three times: 687 × 687 × 687 = 324,631,023.

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

Therefore, the volume of the cube is 324,631,023 cm³.

Well explained 👍

Problem 5

Estimate the cube of 686.5 using the cube of 687.

Okay, lets begin

The cube of 686.5 is approximately 324,631,023.

Explanation

First, identify the cube of 687, The cube of 687 is 687³ = 324,631,023.

Since 686.5 is only a tiny bit less than 687, the cube of 686.5 will be almost the same as the cube of 687.

The cube of 686.5 is approximately 324,631,023 because the difference between 686.5 and 687 is very small.

So, we can approximate the value as 324,631,023.

Well explained 👍

FAQs on Cube of 687

1.What are the perfect cubes up to 687?

The perfect cubes up to 687 are 1, 8, 27, 64, 125, 216, 343, 512, and 729.

2.How do you calculate 687³?

To calculate 687³, use the multiplication method, 687 × 687 × 687, which equals 324,631,023.

3.What is the meaning of 687³?

687³ means 687 multiplied by itself three times, or 687 × 687 × 687.

4.What is the cube root of 687?

5.Is 687 a perfect cube?

No, 687 is not a perfect cube because no integer multiplied by itself three times equals 687.

Important Glossaries for Cube of 687

  • 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 amount of space occupied by a cube, calculated as the cube of its side length.

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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.

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: He loves to play the quiz with kids through algebra to make kids love it.