Do you know what is a cube? Have you find a cube for any number! If not, let us find how to calculate cubes for numbers. Basically, a cube is a number acquired by multiplying the number three times. Thus, the number(x) becomes x³ or x- cube. There is a difference between cube and cube root whereas cube root is the reverse process of the cube of a number and it is denoted by ∛.

Usually, in mathematics, we run mostly with squares and cubes of numbers in arithmetic operations. On this page, 5th Grade Math students will go through more about the cube of numbers, a perfect cube, a cube of negative numbers, and cubes of rational numbers, etc.

Do Check:

- Volume of Cubes and Cuboids
- Worksheet on Volume of a Cube and Cuboid

## Cube – Definition

When an integer is multiplied by three times itself and the resultant product of a number is its cube number. If you consider a number n, then the formula of a cube of a number n is n × n × n = n³ because n is a natural number. In other words, we can say a number raised its exponent by 3 is called the cube of a number. For example, to find the cube of a number 5, we write as 5 × 5 × 5 = 125 and says as the cube of number 5 is 125.

We can also write a cube of the number 6 as 6³ in the exponent form and read 6- cubed. For example, to find 7³, first, we calculate 7 × 7 = 49 and next we calculate 49 × 7 = 343. Thus, we say that 343 is the cube of a number 7. It is to be emphasized that the number obtained using a cube formula is the perfect cube number. The cube is also known as the number which is calculated by its square.

### Cube of a Number Examples

(i) 2³ = (2 × 2 × 2) = 8, here 8 is the cube of 2.

(ii) 3³ = (3 × 3 × 3) = 27, here 27 is the cube of 3.

(iii) 4 × 4 × 4 = 64, here 64 is the cube of 4.

### Perfect Cube

A perfect cube is a number that is similar to the number, multiplied by itself three times or with three same or equal integers. If m is a perfect cube of n, then m = n³. Thus, if we take the cube root of a perfect cube, we get a natural number but not any fraction number. Therefore, ∛m = n. For example, 8 is a perfect cube because ∛8 = 2.

For instance, 125 is a perfect cube because 5³ = 5 × 5 × 5 = 125 where 123 is not a perfect cube because there is no number that comes when the number multiplied three times gives the product 123. The following table shows the perfect cubes of the first 10 natural numbers.

### Cubes of Negative Integers

Cube of any negative integer will always be a negative integer, where the cube of any positive number results always a positive number, there a negative integer product will always give a product of negative integer because when a negative number is calculated by the same number three times, it results in a negative number.

Examples of a cube of negative integers when a number is calculated thrice are as such;

(-1)³ = (-1) × (-1) × (-1) = -1,

(-2)³ = (-2) × (-2) × (-2) = -8

(-3)³ = (-3) × (-3) × (-3) = -27, etc.

### Cubes of Numbers from 1 to 25 Chart

The below table gives the cube values from 1 to 25 numbers along with their notations. These numbers will help the children in solving the numerical problems accurately.

Number |
Multiplying Three Times Itself |
Cube of a Number (x^{3}) |

1 | 1× 1× 1 | 1 |

2 | 2× 2× 2 | 8 |

3 | 3× 3× 3 | 27 |

4 | 4× 4× 4 | 64 |

5 | 5× 5× 5 | 125 |

6 | 6× 6× 6 | 216 |

7 | 7× 7× 7 | 343 |

8 | 8× 8× 8 | 512 |

9 | 9× 9× 9 | 729 |

10 | 10× 10× 10 | 1000 |

11 | 11× 11× 11 | 1331 |

12 | 12× 12× 12 | 1728 |

13 | 13× 13× 13 | 2197 |

14 | 14× 14× 14 | 2744 |

15 | 15× 15× 15 | 3375 |

16 | 16× 16× 16 | 4096 |

17 | 17× 17× 17 | 4913 |

18 | 18× 18× 18 | 5832 |

19 | 19× 19× 19 | 6859 |

20 | 20× 20× 20 | 8000 |

21 | 21× 21× 21 | 9261 |

22 | 22× 22× 22 | 10648 |

23 | 23× 23× 23 | 12167 |

24 | 24× 24× 24 | 13824 |

25 | 25× 25× 25 | 15625 |

### Properties of a Cube

The following are some properties of a cube of numbers where students should remember while doing any cube for an integer.

**(i)** The cube of even natural numbers is always even.

**(ii)** The cube of odd natural numbers is always odd.

**(iii)** The sum of the cubes of first n natural numbers is equal to the square of their sum.

**(iv)** Cubes of the numbers ending in digits 1, 4, 5, 6, and 9 are the numbers ending in the same digit. For example, 1³=1, 4³=64, 5³=125, 6³=216, and 9³=729.

### Cubes of Numbers 1 to 50 PDF Download

The following list helps the children while solving the problems with arithmetic operations. Children can refer to this list of cubes 1 to 50 to solve the problems accurately.

### Examples of Cube of Numbers

**Example 1: **

Find the cube of each of the following numbers

(i) 55 (ii) -41 (iii) 3.5

**Solution: **

**(i) **Given number is 84

To get the cube of 84, we use the formula

n³ = n × n × n

55 = 55 × 55 × 55 = 1,66,375

Hence, the cube of the number 55 is **1,66,375**.

**(ii) **Given number is -41

The number given is a negative integer and the resultant answer is also a negative integer because it is calculated three times and gives a negative integer.

-41 = -41 × -41 × -41 = -68,921.

Thus, the cube of a number -41 is **-68,921**.

**(iii) **3.5 is a given number

When a decimal number is cubed we convert the decimal number into a fraction number.

(3.5)³ = (35/10)³

= (7/2)³

= 7³/2³

= (7× 7× 7)/(2× 2× 2)

= 343/8.

**Example 2: **

What is the value of x if x³ = 64?

**Solution: **

The formula to calculate the cube is

*x*³ = *x* × *x* ×* x*

Here, x³ = 64

x = ∛64 = 4

Therefore, **x=****4**.

**Example 3: **

Find out the cube numbers 7 and 12. Also, find the sum of the cube numbers?

**Solution: **

Firstly, we find the cubed numbers 7 and 12.

The cube number 7 is 7 × 7 × 7 = 343.

The cube number 12 is 12 × 12 × 12 = 1728.

Now, we have to find the sum of the cubed numbers.

i.e., 7³ + 12³ = 343 + 1728 = 2071.

As a result, Sum of the cube numbers is **2,071.**

### FAQ’s on Cubes

**1. What is a Cube?**

A cube is a number where it is multiplied thrice by itself. The symbol for the cubed is ³. For example, to get 5³ we multiply 5 three times itself i.e., 5 × 5 × 5 = 125.

**2. What are the cube numbers from 1 to 10?**

The cubed numbers from 1 to 10 are 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000.

**3. Is 600 is a perfect cube?**

To know 600 is a perfect cube or not. We have to find the multiplies of 600.

The multiplies of 600 are

2× 2× 2× 3× 5× 5 are multiplies of 600.

2³ × 3 × 5² = 600.

Therefore, 600 is not a perfect cube because all the factors are not multiple of three.

**4. Which are the perfect cubes among the numbers 343, 576, 2197?**

Among the given numbers 343 and 2197 are the perfect cubes because 7× 7× 7 = 343 and 13× 13× 13 =2197. Whereas 576 is the perfect square number i.e., 24× 24 = 576.