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# Cube Numbers

Cube numbers are numbers obtained by multiplying a whole number thrice. Exploring cube numbers deepens one’s understanding of arithmetic and number patterns and lays a foundation for more advanced mathematical concepts.

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## What are Cube Numbers?

Cube numbers involve raising a number to the power of three. When a whole number is multiplied thrice, the resulting value is known as a cube number. The symbol for cubed is 3.

If we have an integer “n,” its cube is represented as “n3,” and it can be calculated as n × n × n

For example, if we take the number 2 and cube it, we get 23 , which equals 8. Similarly, the cube of 3 (33) is 27, and the cube of 4 (43) is 64, and so on.

Cube numbers can be both positive and negative. Whether a cube number is positive or negative depends on the cubed original number.  we cube a negative number and raise it to an odd exponent (3).

In mathematics, an odd exponent preserves the sign of the base number. If the base number is negative, the result will also be negative.

Example: (-6)3 = – 6 × – 6 × – 6 = – 216 (three negative signs multiplied by each other, resulting in a negative sign).

In contrast, the result would be positive if you raise a negative number to an even exponent, such as squaring it (raising it to the power of 2). This is because squaring an integer eliminates the negative sign due to the even exponent.

Cube Numbers Facts

1. When even numbers are cubed, the result remains even.

Example:

• The cube of 2:  23 = 8 (both 2 and 8 are even)
• The cube of 4:  43 = 64 (both 4 and 64 are even)

1. When odd numbers are cubed, the result will always be odd.

Example:

• The cube of 1: 13 = 1 (both 1 and the result 1 are odd)
• The cube of 3: 33 = 27 (both 3 and the result 27 are odd)

1. The last digit of the cube remains the same as the last digit of the original number.

Example: The cube of number 4 is 64, a cube of number 5 is 125

However, there are exceptions for the numbers 2, 8, 3, and 27.

Example: The cube of number 2 is 8 and the cube of number 3 is 27 similarly the cube of number 8 is 512, and cube of number 7 is 343

1. Perfect cubes can be expressed as a sum of consecutive odd numbers.

Example: The cube of 2 is 8 and can be represented as 3 + 5 = 8 (sum of two consecutive odd numbers).

The cube of 3 is 27 can be represented as  7 + 9 + 11 = 27 (sum of three consecutive odd numbers).

1. The cube of a positive number is positive, and the cube of a negative number is negative. This is because raising a negative number to an odd power maintains its negative sign.

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Question

1: Calculate the cube of 5.

2: List the first four cube numbers.

1. 2197 is the cube of which number?

4: Express 64 as a sum of consecutive odd numbers.

Solutions

1: The cube of 5 is calculated by raising 5 to the power of 3.

53 = 5 × 5 × 5 = 125

2: The first four cube numbers are:

13 = 1

23 = 8

33 = 27

43 = 64

3: 2197 is the cube of 13

13 x 13 x 13 = 2197

4: Let’s find consecutive odd numbers that sum up to 64

1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64

## FAQs

#### What is a cube number?

A cube number is a number that results from multiplying a number by itself twice (raising it to the power of 3). It is written as n3, where “n” is the original number. For example, 23 is a cube number, and the result is 8.

#### How do you calculate the cube of a number?

To calculate the cube of a number, you multiply the number by itself twice. Mathematically, it’s expressed as n3, where “n” is the number. For example, to find the cube of 4, you would multiply 4 by 4 and then by 4 again, resulting in 43 = 64.

#### What is the difference between a square number and a cube number?

A square number is the result of multiplying a number by itself once (n2), while a cube number is the result of multiplying a number by itself twice (n3). A square number is the second power (squared), and a cube number is the third power (cubed) of a number.

#### What is the formula for finding the cube of a number?

The formula for finding the cube of a number “n” is simply n3. You raise the number to the power of 3 to calculate its cube.

#### Can negative numbers be cube numbers?

Yes, negative numbers can be cube numbers. When you cube a negative number, you get a negative cube number. For example, (-3)3 equals -27.

#### What are the first few cube numbers?

The first few cube numbers are 1, 8, 27, 64, 125, 216, 343, and so on. Each of these numbers is the cube of a positive integer.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

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