Cube of -8
2026-02-28 01:16 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-minus-8

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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 -8.

Cube of -8

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 multiplying a negative number by itself three times results in a negative number. The cube of -8 can be written as (-8)^3, which is the exponential form. Or it can also be written in arithmetic form as -8 × -8 × -8.

How to Calculate the Value of Cube of -8

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 (a^3), 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. By Multiplication Method Using a Formula 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. (-8)^3 = -8 × -8 × -8 Step 2: You get -512 as the answer. Hence, the cube of -8 is -512.

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Using a Formula (a^3)

The formula (a + b)^3 is a binomial formula for finding the cube of a number. The formula is expanded as a^3 + 3a^2b + 3ab^2 + b^3. Step 1: Split the number -8 into two parts, such as -10 and +2. Let a = -10 and b = 2, so a + b = -8 Step 2: Now, apply the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Step 3: Calculate each term a^3 = (-10)^3 3a^2b = 3 × (-10)^2 × 2 3ab^2 = 3 × (-10) × 2^2 b^3 = 2^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-10 + 2)^3 = (-10)^3 + 3 × (-10)^2 × 2 + 3 × (-10) × 2^2 + 2^3 (-8)^3 = -1000 + 600 - 120 + 8 (-8)^3 = -512 Step 5: Hence, the cube of -8 is -512.

Using a Calculator

To find the cube of -8 using a calculator, input the number -8 and use the cube function (if available) or multiply -8 × -8 × -8. This operation calculates the value of (-8)^3, resulting in -512. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Press the negative sign followed by 8 Step 3: If the calculator has a cube function, press it to calculate (-8)^3. Step 4: If there is no cube function on the calculator, simply multiply -8 three times manually. Step 5: The calculator will display -512.

Tips and Tricks for the Cube of -8

The cube of any even number is always even, while the cube of any odd number is always odd. 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 -8

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:

Problem 1

What is the cube and cube root of -8?

Okay, lets begin

The cube of -8 is -512 and the cube root of -8 is -2.

Explanation

First, let’s find the cube of -8. We know that the cube of a number is x^3 = y Where x is the given number, and y is the cubed value of that number So, we get (-8)^3 = -512 Next, we must find the cube root of -8 We know that the cube root of a number ‘x’ is such that ∛x = y Where ‘x’ is the given number, and y is the cube root value of the number So, we get ∛-8 = -2 Hence the cube of -8 is -512 and the cube root of -8 is -2.

Well explained 👍

Problem 2

If the side length of a cube is -8 cm, what is the volume?

Okay, lets begin

The volume is -512 cm^3.

Explanation

Use the volume formula for a cube V = Side^3. Substitute -8 for the side length: V = (-8)^3 = -512 cm^3.

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Problem 3

How much smaller is (-8)^3 than (-7)^3?

Okay, lets begin

(-8)^3 - (-7)^3 = -169.

Explanation

First, find the cube of (-8)^3, which is -512 Next, find the cube of (-7)^3, which is -343 Now, find the difference between them using the subtraction method. -512 - (-343) = -512 + 343 = -169 Therefore, (-8)^3 is 169 smaller than (-7)^3.

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Problem 4

If a cube with a side length of -8 cm is compared to a cube with a side length of 2 cm, how much smaller is the volume of the smaller cube?

Okay, lets begin

The volume of the cube with a side length of -8 cm is -512 cm^3.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing -8 means multiplying -8 by itself three times: -8 × -8 = 64, and then 64 × -8 = -512. The unit of volume is cubic centimeters (cm^3) because we are calculating the space inside the cube. Therefore, the volume of the cube is -512 cm^3.

Well explained 👍

Problem 5

Estimate the cube of -8.1 using the cube of -8.

Okay, lets begin

The cube of -8.1 is approximately -531.

Explanation

First, identify the cube of -8, The cube of -8 is (-8)^3 = -512. Since -8.1 is only a tiny bit less than -8, the cube of -8.1 will be almost the same as the cube of -8. The cube of -8.1 is approximately -531 because the difference between -8.1 and -8 is very small. So, we can approximate the value as -531.

Well explained 👍

FAQs on Cube of -8

1.What are the perfect cubes up to 8?

The perfect cubes up to 8 are 1, 8, and -8.

2.How do you calculate (-8)^3?

To calculate (-8)^3, use the multiplication method: -8 × -8 × -8, which equals -512.

3.What is the meaning of (-8)^3?

(-8)^3 means -8 multiplied by itself three times, or -8 × -8 × -8.

4.What is the cube root of -8?

5.Is -8 a perfect cube?

Yes, -8 is a perfect cube because it is the cube of -2, i.e., (-2)^3 = -8.

Important Glossaries for Cube of -8

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, 2^3 represents 2 × 2 × 2 equals 8. Negative Cube: The result of cubing a negative number, which is always negative since multiplying a negative number by itself three times results in a negative number. Perfect Cube: A number that can be expressed as the cube of an integer. For example, 8 is a perfect cube since it is 2^3.

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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.