Cubes 1 to 30

A cube of a number is the result of multiplying the number by itself three times. The cube of a number n is written as n³, which equals n × n × n.
Using the exponent's formula x³,

Cube of n = x × x × x =x³
21³ = 21 × 21 × 21 = 9261

Cubes from 1 to 30 are the cubes of the numbers, and they are listed as 1 cubed equals 1, 2 cubed equals 8, and so on. The following chart shows all the cubes from 1 to 30:

How to Calculate Cubes 1 to 30?

The cubes from 1 to 30 can be calculated by using two methods, which are

By Multiplying the Number Itself

The cube of any number from 1 to 30 can be easily calculated by multiplying the number itself three times, i.e., the cube of 9 is calculated as,

9³ = 9 × 9 × 9 = 81 × 9 =729
Thus, the cubes of all the numbers from 1 to 30 are calculated.

Using Algebraic Identities

The cube of any number from 1 to 30 can also be calculated by using algebraic identities, as,
29³ = (30-1)³

Using Algebraic Identity, (a - b)³ = a³ - b³ - 3ab(a - b)
29³ = (30)³ - (1)³ - 3(30)(1)(30-1)
⇒ 29³ = 27000 - 1 - 2610
⇒ 29 = 24389

Thus, the cubes of all the numbers from 1 to 30 are calculated.

Solved Questions

Question 1: Find the volume of a cube whose side is 21 cm.

Solution:

Given,
Side of Cube (a) = 21 cm
Volume of Cube = a³ = 21³ = 9261

Thus, the volume of cube is 9261 cm³

Question 2: Simplify (14)³ - (11)³ + (5)³

Solution:

= (14)³ - (11)³ + (5)³
= 2744 - 1331 + 125
= 1538

Question 3: Simplify (24)³ - (9)³ + (15)³

Solution:

= (24)³ - (9)³ + (15)³
= 13824 - 729 + 3375
= 16470

Question 4: Find the difference between the cubes of 7 and 5.

7³ = 343, 5³ = 125
Difference:
343 - 125 = 218

Question 5: Calculate the sum of the cubes of 2 and 4.

2³ = 8, 4³ = 64
Sum:
8 + 64 = 72

Question 6: A cube has a volume of 1000 cubic units. What is the side length?

∛1000 = 10 × 10 × 10 = 10

Practice Questions

Question 1: What is the cube of 4?

Question 2: If the cube of a number is 729 what is the number?

Question 3: Find the difference between the cubes of 5 and 3.

Question 4: A cube has a volume of 512 cubic units. What is the length of one side of the cube?

Question 5: Find the cube root of 27.

Question 6: What is the sum of the cubes of 2 and 3?

Question 7: If the cube of a number is 3375 ,find the number.

Question 8: Determine the cube of 11.

Question 9: Calculate the sum of cubes from 1 to 3.

Question 10: Find the cube of 7 and then subtract 100 from it.

Answer key:

1. 64
2. 9
3. 98
4. 8 units
5. 3
6. 35
7. 15
8. 1331
9. 36
10. 243