The problem is to factor the expression $x^3 - 27$.

1. Problem Description

The problem is to factor the expression $x^3 - 27$.

2. Solution Steps

We recognize that $x^3 - 27$ is a difference of cubes. We can rewrite the expression as $x^3 - 3^3$.

The difference of cubes formula is:

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

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

Applying the formula:

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

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

3. Final Answer

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