Cube of -64
2026-02-28 01:33 Diff
https://brightchamps.com/en-us/math/algebra/cube-of-minus-64

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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 -64.

Cube of -64

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 -64 can be written as (-64)^3, which is the exponential form. Or it can also be written in arithmetic form as, -64 × -64 × -64.

How to Calculate the Value of Cube of -64

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 individuals 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. (-64)^3 = -64 × -64 × -64 Step 2: You get -262,144 as the answer. Hence, the cube of -64 is -262,144.

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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 -64 into two parts, as -60 and -4. Let a = -60 and b = -4, so a + b = -64 Step 2: Now, apply the formula (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 Step 3: Calculate each term a^3 = (-60)^3 3a^2b = 3 × (-60)^2 × (-4) 3ab^2 = 3 × (-60) × (-4)^2 b^3 = (-4)^3 Step 4: Add all the terms together: (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 (-60 - 4)^3 = (-60)^3 + 3 × (-60)^2 × (-4) + 3 × (-60) × (-4)^2 + (-4)^3 (-64)^3 = -216,000 - 43,200 - 2,880 - 64 (-64)^3 = -262,144 Step 5: Hence, the cube of -64 is -262,144.

Using a Calculator

To find the cube of -64 using a calculator, input the number -64 and use the cube function (if available) or multiply -64 × -64 × -64. This operation calculates the value of (-64)^3, resulting in -262,144. It’s a quick way to determine the cube without manual computation. Step 1: Ensure the calculator is functioning properly. Step 2: Input -64 Step 3: If the calculator has a cube function, press it to calculate (-64)^3. Step 4: If there is no cube function on the calculator, simply multiply -64 three times manually. Step 5: The calculator will display -262,144.

Tips and Tricks for the Cube of -64

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 -64

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

Problem 1

What is the cube and cube root of -64?

Okay, lets begin

The cube of -64 is -262,144 and the cube root of -64 is -4.

Explanation

First, let’s find the cube of -64. We know that the cube of a number, such that x^3 = y Where x is the given number, and y is the cubed value of that number So, we get (-64)^3 = -262,144 Next, we must find the cube root of -64 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 ∛(-64) = -4 Hence the cube of -64 is -262,144 and the cube root of -64 is -4.

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Problem 2

If the side length of a cube is -64 cm, what is the volume?

Okay, lets begin

The volume is -262,144 cm³.

Explanation

Use the volume formula for a cube V = Side^3. Substitute -64 for the side length: V = (-64)^3 = -262,144 cm³.

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Problem 3

How much smaller is (-64)^3 than (-60)^3?

Okay, lets begin

(-64)^3 - (-60)^3 = -46,144.

Explanation

First find the cube of (-64)^3, that is -262,144 Next, find the cube of (-60)^3, which is -216,000 Now, find the difference between them using the subtraction method. -262,144 - (-216,000) = -46,144 Therefore, (-64)^3 is 46,144 smaller than (-60)^3.

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Problem 4

If a cube with a side length of -64 cm is compared to a cube with a side length of -4 cm, how much smaller is the volume of the smaller cube?

Okay, lets begin

The volume of the cube with a side length of -64 cm is -262,144 cm³ and the volume of the cube with a side length of -4 cm is -64 cm³. The smaller cube's volume is -64 cm³ smaller.

Explanation

To find the volume of a cube, multiply the side length by itself three times. Cubing -64 means multiplying -64 by itself three times: -64 × -64 = 4,096, and then 4,096 × -64 = -262,144 cm³. For the smaller cube, cubing -4 means multiplying -4 by itself three times: -4 × -4 = 16, and then 16 × -4 = -64 cm³. The difference in volume is -262,144 cm³ - (-64 cm³) = -262,080 cm³.

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Problem 5

Estimate the cube of -63.9 using the cube of -64.

Okay, lets begin

The cube of -63.9 is approximately -262,144.

Explanation

First, identify the cube of -64, The cube of -64 is (-64)^3 = -262,144. Since -63.9 is only a tiny bit more than -64, the cube of -63.9 will be almost the same as the cube of -64. The cube of -63.9 is approximately -262,144 because the difference between -63.9 and -64 is very small. So, we can approximate the value as -262,144.

Well explained 👍

FAQs on Cube of -64

1.What are the perfect cubes up to -64?

The perfect cubes up to -64 are -1, -8, -27, and -64.

2.How do you calculate (-64)^3?

To calculate (-64)^3, use the multiplication method, -64 × -64 × -64, which equals -262,144.

3.What is the meaning of (-64)^3?

(-64)^3 means -64 multiplied by itself three times, or -64 × -64 × -64.

4.What is the cube root of -64?

5.Is -64 a perfect cube?

Yes, -64 is a perfect cube because (-4) multiplied by itself three times equals -64.

Important Glossaries for Cube of -64

1. 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. 2. Cube of a Number: Multiplying a number by itself three times is called the cube of a number. 3. 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, 2^3 represents 2 × 2 × 2 equals 8. 4. Perfect Cube: A number that can be expressed as the product of an integer multiplied by itself three times. 5. Cube Root: The number that, when multiplied by itself three times, gives the original number. For example, the cube root of -64 is -4.

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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.