a^3+b^3 Formula
The a^{3 }+ b^{3} formula is called the sum of cubes (of two numbers) formula. It is one of the algebraic identities. It is used to find the sum of cubes of two numbers without actually calculating the cubes. It is used to factorize the binomials of the sum of cubes as well. In this section, we will be discussing the various aspects of the a^{3 }+ b^{3} formula, and understand the identity involved.
What is a^3+b^3 Formula?
The sum of cubes formula or the a^{3 }+ b^{3} formula is very helpful in calculating the cube of two numbers easily where we actually don't calculate the cube of the two numbers separately. The a^{3 }+ b^{3} formula is:
a^{3 }+ b^{3 }= (a + b) (a^{2}  ab + b^{2})
You can remember these signs using the following trick.
If you would like to verify this, you can just multiply (a + b) (a^{2}  ab + b^{2}) and see whether you get a^{3} + b^{3}.

Example 1: Find the value of 102^{3} + 8^{3 }by using the a^3+b^3 formula.
Solution:
To find: 102^{3} + 8^{3}.
Let us assume that a = 102 and b = 8.
We will substitute these in the formula of a^{3} + b^{3 }i.e.,
a^{3 }+ b^{3 }= (a + b) (a^{2}  ab + b^{2})
102^{3}+8^{3} = (102+8)(102^{2}  (102)(8)+8^{2})
= (110) (10404816+64)
= (110)(9652) '
=1061720
Answer: 102^{3} + 8^{3} = 1,061,720.

Example 2: Factorize the expression 8x^{3} + 27 by using the a^3+b^3 formula.
Solution:
To factorize: 8x^{3} + 27.
We will use the a^{3} + b^{3 }formula to factorize this.
We can write the given expression as
8x^{3} + 27 = (2x)^{3} + 3^{3}
We will substitute a = 2x and b = 3 in the formula of a^{3} + b^{3}.
a^{3 }+ b^{3 }= (a + b) (a^{2}  ab + b^{2})
(2x)^{3}+3^{3} =(2x+3)((2x)^{2}(2x)(3)+3^{2})
= (2x+3) (4x^{2}6x+9)
Answer: 8x^{3} + 27 = (2x + 3) (4x^{2}  6x + 9).