Cube of 1001
2026-02-28 13:59 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 while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about cubes of 1001.

Cube of 1001

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 1001 can be written as 1001³, which is the exponential form. Or it can also be written in arithmetic form as, 1001 × 1001 × 1001.

How to Calculate the Value of Cube of 1001

In order to check whether a number is a cube number or not, we can use the following three methods: 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 numbers 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. 1001³ = 1001 × 1001 × 1001

Step 2: You get 1,003,003,001 as the answer. Hence, the cube of 1001 is 1,003,003,001.

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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 1001 into two parts. Let a = 1000 and b = 1, so a + b = 1001

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

Step 3: Calculate each term

a³ = 1000³

3a²b = 3 × 1000² × 1

3ab² = 3 × 1000 × 1²

b³ = 1³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(1000 + 1)³ = 1000³ + 3 × 1000² × 1 + 3 × 1000 × 1² + 1³

1001³ = 1,000,000,000 + 3,000,000 + 3,000 + 1

1001³ = 1,003,003,001

Step 5: Hence, the cube of 1001 is 1,003,003,001.

Using a Calculator

To find the cube of 1001 using a calculator, input the number 1001 and use the cube function (if available) or multiply 1001 × 1001 × 1001. This operation calculates the value of 1001³, resulting in 1,003,003,001. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 1, 0, 0, and 1

Step 3: If the calculator has a cube function, press it to calculate 1001³.

Step 4: If there is no cube function on the calculator, simply multiply 1001 three times manually.

Step 5: The calculator will display 1,003,003,001.

Tips and Tricks for the Cube of 1001

  • 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 1001

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 1001?

Okay, lets begin

The cube of 1001 is 1,003,003,001 and the cube root of 1001 is approximately 10.003.

Explanation

First, let’s find the cube of 1001.

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 1001³ = 1,003,003,001

Next, we must find the cube root of 1001.

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 ∛1001 ≈ 10.003

Hence the cube of 1001 is 1,003,003,001 and the cube root of 1001 is approximately 10.003.

Well explained 👍

Problem 2

If the side length of the cube is 1001 cm, what is the volume?

Okay, lets begin

The volume is 1,003,003,001 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 1001 for the side length: V = 1001³ = 1,003,003,001 cm³.

Well explained 👍

Problem 3

How much larger is 1001³ than 999³?

Okay, lets begin

1001³ – 999³ = 6,003,003.

Explanation

First, find the cube of 1001, which is 1,003,003,001.

Next, find the cube of 999, which is 997,002,999.

Now, find the difference between them using the subtraction method. 1,003,003,001 – 997,002,999 = 6,003,003

Therefore, 1001³ is 6,003,003 larger than 999³.

Well explained 👍

Problem 4

If a cube with a side length of 1001 cm is compared to a cube with a side length of 1 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 1001 cm is 1,003,003,001 cm³.

Explanation

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

Cubing 1001 means multiplying 1001 by itself three times: 1001 × 1001 = 1,002,001, and then 1,002,001 × 1001 = 1,003,003,001.

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

Therefore, the volume of the cube is 1,003,003,001 cm³.

Well explained 👍

Problem 5

Estimate the cube 1000.1 using the cube 1001.

Okay, lets begin

The cube of 1000.1 is approximately 1,003,003,001.

Explanation

First, identify the cube of 1001, The cube of 1001 is 1001³ = 1,003,003,001.

Since 1000.1 is only a tiny bit less than 1001, the cube of 1000.1 will be almost the same as the cube of 1001.

The cube of 1000.1 is approximately 1,003,003,001 because the difference between 1000.1 and 1001 is very small.

So, we can approximate the value as 1,003,003,001.

Well explained 👍

FAQs on Cube of 1001

1.What are some perfect cubes up to 1001?

Some perfect cubes up to 1001 include 1, 8, 27, 64, 125, 216, 343, 512, and 729.

2.How do you calculate 1001³?

To calculate 1001³, use the multiplication method, 1001 × 1001 × 1001, which equals 1,003,003,001.

3.What is the meaning of 1001³?

1001³ means 1001 is multiplied by itself three times, or 1001 × 1001 × 1001.

4.What is the cube root of 1001?

The cube root of 1001 is approximately 10.003.

5.Is 1001 a perfect cube?

No, 1001 is not a perfect cube because no integer multiplied by itself three times equals 1001.

Important Glossaries for Cube of 1001

  • Binomial Formula: An algebraic expression used to expand 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.
  • Cube Root: An operation to determine a number that, when cubed, results in a given number. For example, the cube root of 8 is 2.
  • Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself twice, such as 1, 8, 27, etc.

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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.