We are asked to factor the expression $x^3 - 27$.

1. Problem Description

We are asked to factor the expression $x^3 - 27$.

2. Solution Steps

The given expression is a difference of cubes. We can use the formula for factoring the difference of cubes:

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

In this case, $a = x$ and $b = 3$, since $27 = 3^3$.

Applying the formula, we have:

$x^3 - 27 = x^3 - 3^3 = (x - 3)(x^2 + (x)(3) + 3^2)$

Simplifying, we get:

$x^3 - 27 = (x - 3)(x^2 + 3x + 9)$

3. Final Answer

$(x - 3)(x^2 + 3x + 9)$