Cube of 638
2026-02-28 10:56 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 638.

Cube of 638

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 638 can be written as 638³, which is the exponential form. Or it can also be written in arithmetic form as 638 × 638 × 638.

How to Calculate the Value of Cube of 638

To determine 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 three methods help us cube 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 numbers or quantities by combining them through repeated multiplication. It is a fundamental operation that forms the basis for more complex mathematical concepts.

Step 1: Write down the cube of the given number. 638³ = 638 × 638 × 638

Step 2: You get 259,459,192 as the answer. Hence, the cube of 638 is 259,459,192.

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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 638 into two parts. Let a = 630 and b = 8, so a + b = 638

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

Step 3: Calculate each term

a³ = 630³

3a²b = 3 × 630² × 8

3ab² = 3 × 630 × 8²

b³ = 8³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(630 + 8)³ = 630³ + 3 × 630² × 8 + 3 × 630 × 8² + 8³

638³ = 250,047,000 + 95,040 + 12,096 + 512

638³ = 259,459,192

Step 5: Hence, the cube of 638 is 259,459,192.

Using a Calculator

To find the cube of 638 using a calculator, input the number 638 and use the cube function (if available) or multiply 638 × 638 × 638. This operation calculates the value of 638³, resulting in 259,459,192. 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 3 and 8.

Step 3: If the calculator has a cube function, press it to calculate 638³.

Step 4: If there is no cube function on the calculator, simply multiply 638 three times manually.

Step 5: The calculator will display 259,459,192.

Tips and Tricks for the Cube of 638

  • 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 638

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 638?

Okay, lets begin

The cube of 638 is 259,459,192 and the cube root of 638 is 8.594.

Explanation

First, let’s find the cube of 638.

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

So, we get 638³ = 259,459,192.

Next, we must find the cube root of 638. We know that the cube root of a number ‘x’ is such that ³√x = y Where ‘x’ is the given number, and y is the cube root value of the number.

So, we get ³√638 = 8.594

Hence, the cube of 638 is 259,459,192 and the cube root of 638 is approximately 8.594.

Well explained 👍

Problem 2

If the side length of the cube is 638 cm, what is the volume?

Okay, lets begin

The volume is 259,459,192 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 638 for the side length: V = 638³ = 259,459,192 cm³.

Well explained 👍

Problem 3

How much larger is 638³ than 628³?

Okay, lets begin

638³ – 628³ = 37,790,072.

Explanation

First, find the cube of 638³, which is 259,459,192.

Next, find the cube of 628³, which is 221,669,120.

Now, find the difference between them using the subtraction method. 259,459,192 – 221,669,120 = 37,790,072.

Therefore, 638³ is 37,790,072 larger than 628³.

Well explained 👍

Problem 4

If a cube with a side length of 638 cm is compared to a cube with a side length of 38 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 638 cm is 259,459,192 cm³.

Explanation

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

Cubing 638 means multiplying 638 by itself three times: 638 × 638 = 407,044, and then 407,044 × 638 = 259,459,192.

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

Therefore, the volume of the cube is 259,459,192 cm³.

Well explained 👍

Problem 5

Estimate the cube of 637.9 using the cube of 638.

Okay, lets begin

The cube of 637.9 is approximately 259,459,192.

Explanation

First, identify the cube of 638, The cube of 638 is 638³ = 259,459,192.

Since 637.9 is only a tiny bit less than 638, the cube of 637.9 will be almost the same as the cube of 638.

The cube of 637.9 is approximately 259,459,192 because the difference between 637.9 and 638 is very small.

So, we can approximate the value as 259,459,192.

Well explained 👍

FAQs on Cube of 638

1.What are the perfect cubes up to 638?

The perfect cubes up to 638 are 1, 8, 27, 64, 125, 216, 343, and 512.

2.How do you calculate 638³?

To calculate 638³, use the multiplication method: 638 × 638 × 638, which equals 259,459,192.

3.What is the meaning of 638³?

638³ means 638 multiplied by itself three times, or 638 × 638 × 638.

4.What is the cube root of 638?

5.Is 638 a perfect cube?

No, 638 is not a perfect cube because no integer multiplied by itself three times equals 638.

Important Glossaries for Cube of 638

  • 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.
  • Cube Root: The number that, when multiplied by itself three times, equals the original number. For example, the cube root of 8 is 2 because 2 × 2 × 2 equals 8.

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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.