The problem is to factor the expression $x^3 - 8$.

1. Problem Description

The problem is to factor the expression $x^3 - 8$.

2. Solution Steps

We can rewrite the expression as a difference of cubes: $x^3 - 2^3$.

The general formula for factoring a difference of cubes is:

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

In our case, $a = x$ and $b = 2$. Substituting these values into the formula:

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

Simplifying:

$x^3 - 8 = (x - 2)(x^2 + 2x + 4)$

The quadratic expression $x^2 + 2x + 4$ cannot be factored further using real numbers because its discriminant is $2^2 - 4(1)(4) = 4 - 16 = -12$, which is negative.

3. Final Answer

$(x - 2)(x^2 + 2x + 4)$