The problem requires us to factor the expression $8x^3 - 27y^3$.

1. Problem Description

The problem requires us to factor the expression $8x^3 - 27y^3$.

2. Solution Steps

We can recognize that the given expression is a difference of cubes.

The general formula for the difference of cubes is

$a^3 - b^3 = (a-b)(a^2 + ab + b^2)$

In our case, we have $8x^3 - 27y^3$.

We can rewrite this as $(2x)^3 - (3y)^3$.

Let $a = 2x$ and $b = 3y$.

Then, we can apply the difference of cubes formula:

$(2x)^3 - (3y)^3 = (2x - 3y)((2x)^2 + (2x)(3y) + (3y)^2)$

$(2x)^3 - (3y)^3 = (2x - 3y)(4x^2 + 6xy + 9y^2)$

3. Final Answer

The factored form of $8x^3 - 27y^3$ is $(2x - 3y)(4x^2 + 6xy + 9y^2)$.