Cube Numbers

When an integer is multiplied by itself three times the resultant number is known as its cube number. Basically, a cube number is a number obtained by the product of three same numbers. In geometry, the volume of a cube is the finest example of a cube number.

When an integer is multiplied by the same integer three times, the resultant number is known as a cube number. Cube numbers are also known as perfect cubes. For example, 5 × 5 × 5 = 5³ = 125. Thus, a cube number is a number with the exponential power of 3, or the multiplication of a number by the same number three times. Cube numbers of positive numbers are positive and cube numbers of negative numbers are negative because when a negative number is multiplied by the same negative number three times, it results in a negative number. For example, (-7)³ = - 7 × - 7 × - 7 = - 343 (three negative signs multiplied by each other, results in a negative sign). We can see when we multiply -7 three times the result is - 343 and it is a negative cube number. Here are some examples of cube numbers.

• - 8 × - 8 × - 8 = -8³ = - 512
• 12 × 12 × 12 = 1728
• - 2 × - 2 × - 2 = -8
• 34 × 34 × 34 = 39304

In geometry, the volume of a cube = length × width × height. Since it's a cube, the length, width, and height are all equal in the cube. Thus, the volume of the cube = a³, where a = length = height = width. This means the volume of a cube is a cube number.

The points listed below are the facts of cube numbers.

• There will be no change in the last digit of a number and the last digit of the cube number of the number, except 2 will change to 8 and 8 will change to 2 and 3 will change to 7, and 7 will change to 3. For 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, and so on. Let's take an example of numbers other than 2,3,7 and 8. The cube of number 4 is 64, a cube of number 5 is 125, a cube of number 14 is 2744, and so on. We can see that the last digits of a cube number and the number which is cubed are the same.
• When even numbers are cubed, the result will be an even number. For example, 2³ = 8, 4³ = 64
• When odd numbers are cubed, the result will be an odd number. For example, 3³ = 27, 5³ = 125
• Perfect cube numbers can be both positive or negative integers. For example, both 8 and - 8 are the perfect cubes of 2 and - 2 respectively.
• Perfect cubes can be expressed as a sum of consecutive odd numbers. For example, 8 is a cube number of 2 and it can be expressed as a sum of consecutive odd numbers 3 + 5 = 8; 27 is a cube number of 3 and it can be expressed as a sum of consecutive odd numbers 7 + 9 + 11 = 27

Use the given list of cube numbers from 1 to 50 to solve problems related to cube numbers.

Related Articles

Check out the interesting topics related to cube numbers.

• Perfect Cube
• Cubes 1 to 100
• Cube 1 to 30
• Cube 1 to 50
• Cube 1 to 20

What are Cube Numbers in Maths?

The number that is obtained by multiplying an integer to itself three times is known as a cube number. Suppose, 'n' is an integer, then the cube number of 'n' is (n × n × n) or n³. For example, in 2 × 2 × 2 = 8, 8 is a cube number of 2.

What is the Sum of all Perfect Cube Numbers from 1 to 50?

The sum of all cube numbers comes between 1 to 50 is [1 + 8 + 27] = 36. There are only three cube numbers that come under the counting of 1 to 50. The cube number of 3 is 27 and the cube number of 4 is 64 which is more than 50.

What are the Perfect Cube Numbers Comes Under 1 to 100?

The cube numbers that come under 1 to 100 are 1, 8, 27, and 64 because the cube number of 4 is 64 and the cube number of 5 is 125 which is more than 100.

What are the First 11 Cube Numbers?

The first 11 cube numbers are 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000.

Is 28 a Cube Number?

No, 28 is not a cube number. If you start cubing one-digit numbers you will find that 3 × 3 × 3 = 27 and 4 × 4 × 4 = 64 so, after 27 the next cube number is 64. Thus, 28 is not a cube number.

What Cube& Number is Closest to 120?

The closest cube number to 120 is 125. When the number 5 is multiplied by itself three times it gives the cube number 125 [5 × 5 × 5 = 125] and it is closest to 120.

What is the Relation Between Perfect Cube Numbers and Perfect Cube Root?

A perfect cube number like 1331 has a perfect cube root that is 11. So, the cube root of 1331 is 11. The number that we cube to get cube numbers is the cube root of a cube number. For example, in 3 × 3 × 3 = 27, 3 is the cube root of 27, and 27 is the cube number of 3. Perfect cube numbers and perfect cube roots mean that the result will always be a whole number. For example, 8 is a perfect cube number as its cube root is a whole number 2.