Sum of Cubes Formula
The formula to find the addition of two polynomials, a^{3 }+ b^{3} is known as the sum of cubes formula. Let's learn more about the sum of cubes formula with a few solved examples. This factoring formula comes in very handy when solving algebraic expressions of various types. Memorizing this formula is also easy and can be done within a matter of minutes. It is very similar to the difference in cubes formula as well.
What Is the Sum of Cubes Formula?
In this section, let us go further and understand what exactly does it mean when some is referring to the sum of cubes. The formula to the sum of cubes formula is given as:
a^{3}+b^{3} = (a+b)(a^{2}ab+b^{2})
where,

a is the first variable

b is the second variable
Let us now see some examples to understand the concept of adding the cubes of a number, better.

Example1: Use the sum of cubes formula to find the factor of 216x^{3 }+ 64.
To find: Factor of 216x^{3 }+ 64, using the sum of cubes formula.
216x^{3}+ 64 = (6x)^{3} + 4^{3}
Using the sum of cubes formula,
a^{3}+b^{3} = (a + b)(a^{2 } ab + b^{2})
Put the values,
(6x)^{3} + 4^{3} = (6x + 4)((6x)^{2 } 6x × 4 + 4^{2})
(6x)^{3} + 4^{3} = (6x + 4)(36x^{2 } 24x +16)
(6x)^{3} + 4^{3} = 4(6x + 4)(9x^{2 } 6x + 4)
Answer: The factor of 216x^{3} + 64 is 4(6x + 4)(9x^{2 } 6x + 4).

Example 2: Find the factor of 8x^{3} + 125y^{3}.
To find: Factor of 8x^{3} + 125y^{3}, using the sum of cubes formula.
8x^{3} + 125y^{3} = (2x)^{3} + (5y)^{3}
Using the sum of cubes formula,
a^{3}+b^{3} = (a + b)(a^{2 } ab + b^{2})
Put the values,
(2x)^{3} + (5y)^{3} = (2x + 5y)((2x)^{2} – (2x)(5y) + (5y)^{2}
(2x)^{3} + (5y)^{3 }= (2x + 5y)(4x^{2} – 10xy + 25y^{2})
Answer: The factor of 8x^{3} + 125y^{3} is (2x + 5y)(4x^{2} – 10xy + 25y^{2}).