1. **State the problem:** Factor the expression $x^3 - 9$. 2. **Recognize the form:** The expression is a difference of cubes if rewritten as $x^3 - 3^3$. 3. **Apply the difference of cubes formula:** $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ where $a = x$ and $b = 3$. 4. **Substitute values:** $$(x - 3)(x^2 + 3x + 9)$$ 5. **Final answer:** The factorization of $x^3 - 9$ is $$\boxed{(x - 3)(x^2 + 3x + 9)}$$