Last updated on July 4th, 2025
When a number is multiplied by itself three times, the product is called a cube number, also known as a perfect cube. Cube numbers are used in calculating volume in architecture and engineering. In this article, we will learn about cube numbers, their properties, and their importance.
Cube numbers in math are the result of a number being multiplied by itself three times.
It can be expressed as n3 = n × n × n, where n is the base number. The cube is related to the 3D shape, so we call it as cube. We call it a cube because it relates to the 3D shape, where all the sides of a cube are equal.
When a positive number is cubed, the result will always be positive. In the case of negative numbers, a negative number cubed will always remain negative.
The history of cube root can be traced back to the Babylonians and the ancient Egyptians civilizations. Around 2000 BCE, the Babylonians were the first to solve cubic equations and study geometric shapes, although they used them for practical uses like calculating volume.
The Greeks eventually created a term for the cubes of numbers, which comes from the word ‘Kybos’ when translated, meaning a three-dimensional solid with three sides. Greek mathematicians like Euclid proved the relationships between cube numbers and other geometric figures by using Pythagorean triples and geometric proofs. Eventually, during the 3rd Century, the father of algebra Diophantus, laid the groundwork for future studies by exploring cubes numbers and gave the connections between cubes and algebra.
Today, cube numbers have become a very important concept in topics such as geometry, number theory, and algebra.
We know that a cube number is the product of a number that is multiplied by itself three times. Here are a few properties of cube numbers:
A cube number comes in two types:
Small Cube Numbers: Cubing small integers results in small cube numbers. Usually easy to calculate and used in basic math.
Example: 33 = 27, 43 = 64, and so on.
Large Cube Numbers: Cubing large numbers results in larger numbers.
Example: 203 = 8000, 303 = 27000, and so on.
To learn the fundamental concepts in mathematics, it is important for the students to understand the cube numbers .
In cube numbers, we have large and small cube numbers. However, there are numbers that have a relationship with cube numbers and some that do not.
Learning cubes of numbers can be easy, but there is a way to make learning much easier with the help of these tips and tricks.
When learning cube numbers, students can make small mistakes. Here are some of the common mistakes and ways to avoid the mistakes:
In real-life we use cube numbers not only in mathematics but also in solving practical problems related to engineering and architecture. Here are a few real-world applications:
Find the cube of -3.
The cube of -3 is -27.
To find the cube, we use the formula:
n3 = n × n × n
Write n = -3
(-3)3 = (-3) × (-3) × (-3) = -27.
When cubing a negative number, we always get a negative number.
You are designing a storage box in the shape of a cube. If each side of the box is 7 meters long, what is the volume of the box?
The volume of the box is 343 cubic meters
The length of the cube is 7 meters
We use the formula n3 = n × n × n
73 = 7 × 7 × 7 = 343 cubic meters.
Find the cube of the sum of 8 and 4.
The cube of the sum of 8 and 4 is 1,728.
To find the sum of cube of 8 and 4,
(8 + 4)3 = 123
Now, calculate the cube of 12:
123 = 12 × 12 × 12 = 1,728.
You are constructing a cube-shaped garden. If each side of the garden is 5 feet long, how much soil do you need to fill it?
You will need 125 cubic feet of soil
The volume of the garden with side length of 5 feet is:
53 = 5 × 5 × 5 = 125 cubic feet
A cube-shaped ice tray has sides of 3 inches. How much ice will the tray hold?
The tray will hold 27 cubic inches of ice.
33 = 3 × 3 × 3 = 27 cubic inches.
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.
: He loves to play the quiz with kids through algebra to make kids love it.