Cube of 164
2026-02-28 11:31 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 that number. Cubing is used while comparing sizes of objects or things with cubic measurements. In this topic, we shall learn about the cube of 164.

Cube of 164

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 164 can be written as 164³, which is the exponential form. Or it can also be written in arithmetic form as 164 × 164 × 164.

How to Calculate the Value of Cube of 164

In order to check whether a number is a cube number or not, we can use the following three methods: the 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 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. 164³ = 164 × 164 × 164

Step 2: You get 4,398,304 as the answer. Hence, the cube of 164 is 4,398,304.

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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 164 into two parts, such as a = 160 and b = 4, so a + b = 164.

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

Step 3: Calculate each term: a³ = 160³

3a²b = 3 × 160² × 4

3ab² = 3 × 160 × 4²

b³ = 4³

Step 4: Add all the terms together: (a + b)³ = a³ + 3a²b + 3ab² + b³

(160 + 4)³ = 160³ + 3 × 160² × 4 + 3 × 160 × 4² + 4³

164³ = 4,096,000 + 307,200 + 7,680 + 64

164³ = 4,398,304

Step 5: Hence, the cube of 164 is 4,398,304.

Using a Calculator

To find the cube of 164 using a calculator, input the number 164 and use the cube function (if available) or multiply 164 × 164 × 164. This operation calculates the value of 164³, resulting in 4,398,304. It’s a quick way to determine the cube without manual computation.

Step 1: Ensure the calculator is functioning properly.

Step 2: Press 1 followed by 6 and 4.

Step 3: If the calculator has a cube function, press it to calculate 164³.

Step 4: If there is no cube function on the calculator, simply multiply 164 three times manually.

Step 5: The calculator will display 4,398,304.

Tips and Tricks for the Cube of 164

  • 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 164

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 164?

Okay, lets begin

The cube of 164 is 4,398,304 and the cube root of 164 is approximately 5.493.

Explanation

First, let’s find the cube of 164.

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 164³ = 4,398,304.

Next, we must find the cube root of 164.

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 ∛164 ≈ 5.493.

Hence, the cube of 164 is 4,398,304 and the cube root of 164 is approximately 5.493.

Well explained 👍

Problem 2

If the side length of the cube is 164 cm, what is the volume?

Okay, lets begin

The volume is 4,398,304 cm³.

Explanation

Use the volume formula for a cube V = Side³.

Substitute 164 for the side length: V = 164³ = 4,398,304 cm³.

Well explained 👍

Problem 3

How much larger is 164³ than 80³?

Okay, lets begin

164³ – 80³ = 4,185,504.

Explanation

First find the cube of 164³, which is 4,398,304. Next, find the cube of 80³, which is 512,000.

Now, find the difference between them using the subtraction method:

4,398,304 – 512,000 = 4,185,504.

Therefore, 164³ is 4,185,504 larger than 80³.

Well explained 👍

Problem 4

If a cube with a side length of 164 cm is compared to a cube with a side length of 20 cm, how much larger is the volume of the larger cube?

Okay, lets begin

The volume of the cube with a side length of 164 cm is 4,398,304 cm³.

Explanation

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

Cubing 164 means multiplying 164 by itself three times:

164 × 164 = 26,896, and then 26,896 × 164 = 4,398,304.

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

Therefore, the volume of the cube is 4,398,304 cm³.

Well explained 👍

Problem 5

Estimate the cube 163.9 using the cube 164.

Okay, lets begin

The cube of 163.9 is approximately 4,398,304.

Explanation

First, identify the cube of 164.

The cube of 164 is 164³ = 4,398,304.

Since 163.9 is only a tiny bit less than 164, the cube of 163.9 will be almost the same as the cube of 164.

The cube of 163.9 is approximately 4,398,304 because the difference between 163.9 and 164 is very small.

So, we can approximate the value as 4,398,304.

Well explained 👍

FAQs on Cube of 164

1.What are the perfect cubes up to 164?

The perfect cubes up to 164 are 1, 8, 27, 64, and 125.

2.How do you calculate 164³?

To calculate 164³, use the multiplication method, 164 × 164 × 164, which equals 4,398,304.

3.What is the meaning of 164³?

164³ means 164 multiplied by itself three times, or 164 × 164 × 164.

4.What is the cube root of 164?

5.Is 164 a perfect cube?

No, 164 is not a perfect cube because no integer multiplied by itself three times equals 164.

Important Glossaries for Cube of 164

  • 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 equals 8.
  • Cube Root: The cube root of a number is a value that, when multiplied by itself three times, gives the original number.
  • Volume: The amount of space occupied by a 3-dimensional object, often measured in cubic units, such as cubic centimeters (cm³).

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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.