Cube of 871
2026-02-28 10:48 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 871.

Cube of 871

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 because a negative number multiplied by itself three times results in a negative number.

The cube of 871 can be written as 871³, which is the exponential form. Or it can also be written in arithmetic form as, 871 × 871 × 871.

How to Calculate the Value of Cube of 871

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 methods will help cube numbers faster and easier without confusion or getting stuck while finding 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 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. 871³ = 871 × 871 × 871

Step 2: You get 660,422,311 as the answer. Hence, the cube of 871 is 660,422,311.

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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 871 into two parts, as 870 and 1. Let a = 870 and b = 1, so a + b = 871

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

Step 3: Calculate each term

a³ = 870³

3a²b = 3 × 870² × 1

3ab² = 3 × 870 × 1²

b³ = 1³

Step 4: Add all the terms together:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(870 + 1)³ = 870³ + 3 × 870² × 1 + 3 × 870 × 1² + 1³

871³ = 658503000 + 2265900 + 2610 + 1

871³ = 660,422,311

Step 5: Hence, the cube of 871 is 660,422,311.

Using a Calculator

To find the cube of 871 using a calculator, input the number 871 and use the cube function (if available) or multiply 871 × 871 × 871. This operation calculates the value of 871³, resulting in 660,422,311. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 8 followed by 7 and 1

Step 3: If the calculator has a cube function, press it to calculate 871³.

Step 4: If there is no cube function on the calculator, simply multiply 871 three times manually.

Step 5: The calculator will display 660,422,311.

Tips and Tricks for the Cube of 871

  • 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 871

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 871?

Okay, lets begin

The cube of 871 is 660,422,311 and the cube root of 871 is approximately 9.545.

Explanation

First, let’s find the cube of 871.

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 871³ = 660,422,311

Next, we must find the cube root of 871

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 ∛871 ≈ 9.545

Hence, the cube of 871 is 660,422,311 and the cube root of 871 is approximately 9.545.

Well explained 👍

Problem 2

If the side length of the cube is 871 cm, what is the volume?

Okay, lets begin

The volume is 660,422,311 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 871 for the side length: V = 871³ = 660,422,311 cm³.

Well explained 👍

Problem 3

How much larger is 871³ than 870³?

Okay, lets begin

871³ – 870³ = 1,919,311.

Explanation

First find the cube of 871, that is 660,422,311

Next, find the cube of 870, which is 658,503,000

Now, find the difference between them using the subtraction method. 660,422,311 – 658,503,000 = 1,919,311

Therefore, 871³ is 1,919,311 larger than 870³.

Well explained 👍

Problem 4

If a cube with a side length of 871 cm is compared to a cube with a side length of 50 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 871 cm is 660,422,311 cm³.

Explanation

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

Cubing 871 means multiplying 871 by itself three times: 871 × 871 = 758,641, and 758,641 × 871 = 660,422,311.

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

Therefore, the volume of the cube is 660,422,311 cm³.

Well explained 👍

Problem 5

Estimate the cube of 870 using the cube of 871.

Okay, lets begin

The cube of 870 is approximately 658,503,000.

Explanation

First, identify the cube of 871, The cube of 871 is 871³ = 660,422,311.

Since 870 is slightly less than 871, the cube of 870 will be slightly less than the cube of 871.

The cube of 870 is approximately 658,503,000 because the number is close to 871.

So, we can approximate the value as 658,503,000.

Well explained 👍

FAQs on Cube of 871

1.What are the perfect cubes up to 871?

The perfect cubes up to 871 are 1, 8, 27, 64, 125, 216, 343, 512, and 729.

2.How do you calculate 871³?

To calculate 871³, use the multiplication method: 871 × 871 × 871, which equals 660,422,311.

3.What is the meaning of 871³?

871³ means 871 multiplied by itself three times, or 871 × 871 × 871.

4.What is the cube root of 871?

5.Is 871 a perfect cube?

No, 871 is not a perfect cube because no integer multiplied by itself three times equals 871.

Important Glossaries for Cube of 871

  • 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.
  • Multiplication Method: A mathematical process used to find the product of numbers or quantities by combining them through repeated addition.
  • Perfect Cube: A number that can be expressed as the cube of an integer.

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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.