Cube of -18
2026-02-28 13:33 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-minus-18

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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 the cube of -18.

Cube of -18

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 -18 can be written as (-18)³, which is the exponential form. Or it can also be written in arithmetic form as -18 × -18 × -18.

How to Calculate the Value of Cube of -18

In order to calculate 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 students 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 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. (-18)³ = -18 × -18 × -18 Step 2: You get -5,832 as the answer. Hence, the cube of -18 is -5,832.

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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 -18 into two parts, as -20 and 2. Let a = -20 and b = 2, so a + b = -18 Step 2: Now, apply the formula (a + b)³ = a³ + 3a²b + 3ab² + b³ Step 3: Calculate each term a³ = (-20)³ 3a²b = 3 × (-20)² × 2 3ab² = 3 × (-20) × 2² b³ = 2³ Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³ (-20 + 2)³ = (-20)³ + 3 × (-20)² × 2 + 3 × (-20) × 2² + 2³ (-18)³ = -8,000 + 2,400 - 240 + 8 (-18)³ = -5,832 Step 5: Hence, the cube of -18 is -5,832.

Using a Calculator

To find the cube of -18 using a calculator, input the number -18 and use the cube function (if available) or multiply -18 × -18 × -18. This operation calculates the value of (-18)³, resulting in -5,832. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input -18 Step 3: If the calculator has a cube function, press it to calculate (-18)³. Step 4: If there is no cube function on the calculator, simply multiply -18 three times manually. Step 5: The calculator will display -5,832.

Tips and Tricks for the Cube of -18

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 -18

There are some typical errors that students might make during the process of cubing a number. Let us take a look at five of the major mistakes that students might make:

Problem 1

What is the cube and cube root of -18?

Okay, lets begin

The cube of -18 is -5,832 and the cube root of -18 is approximately -2.6207.

Explanation

First, let’s find the cube of -18. 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 (-18)³ = -5,832. Next, we must find the cube root of -18. 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√-18 = -2.6207 (approximately). Hence the cube of -18 is -5,832 and the cube root of -18 is approximately -2.6207.

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Problem 2

If the side length of the cube is -18 cm, what is the volume?

Okay, lets begin

The volume is -5,832 cm³.

Explanation

Use the volume formula for a cube V = Side³. Substitute -18 for the side length: V = (-18)³ = -5,832 cm³.

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Problem 3

How much larger is (-18)³ than (-20)³?

Okay, lets begin

(-18)³ – (-20)³ = 2,168.

Explanation

First find the cube of (-18)³, that is -5,832. Next, find the cube of (-20)³, which is -8,000. Now, find the difference between them using the subtraction method. -5,832 - (-8,000) = 2,168. Therefore, (-18)³ is 2,168 larger than (-20)³.

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Problem 4

If a cube with a side length of -18 cm is compared to a cube with a side length of 2 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of -18 cm is -5,832 cm³.

Explanation

To find its volume, we multiply the side length by itself three times (since it’s a 3-dimensional object). Cubing -18 means multiplying -18 by itself three times: -18 × -18 = 324, and then 324 × -18 = -5,832. The unit of volume is cubic centimeters (cm³), because we are calculating the space inside the cube. Therefore, the volume of the cube is -5,832 cm³.

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Problem 5

Estimate the cube of -17.9 using the cube of -18.

Okay, lets begin

The cube of -17.9 is approximately -5,832.

Explanation

First, identify the cube of -18. The cube of -18 is (-18)³ = -5,832. Since -17.9 is only a tiny bit more than -18, the cube of -17.9 will be almost the same as the cube of -18. The cube of -17.9 is approximately -5,832 because the difference between -17.9 and -18 is very small. So, we can approximate the value as -5,832.

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FAQs on Cube of -18

1.What are the perfect cubes up to 18?

The perfect cubes up to 18 are 1 and 8.

2.How do you calculate (-18)³?

To calculate (-18)³, use the multiplication method, -18 × -18 × -18, which equals -5,832.

3.What is the meaning of (-18)³?

(-18)³ means -18 multiplied by itself three times, or -18 × -18 × -18.

4.What is the cube root of -18?

The cube root of -18 is approximately -2.6207.

5.Is -18 a perfect cube?

No, -18 is not a perfect cube because no integer multiplied by itself three times equals -18.

Important Glossaries for Cube of -18

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, which equals 8. Negative Number: A number less than zero, often represented with a minus sign. When raised to an odd power, the result is negative. Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself twice more, such as 1, 8, 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.