1. **State the problem:** Factor the expression $x^3 - b^3$. 2. **Formula used:** The difference of cubes formula is $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ where $a$ and $b$ are any expressions. 3. **Apply the formula:** Here, $a = x$ and $b = b$. 4. **Factorization:** $$x^3 - b^3 = (x - b)(x^2 + xb + b^2)$$ 5. **Explanation:** The difference of cubes factors into a product of a binomial $(x - b)$ and a trinomial $(x^2 + xb + b^2)$. This is a standard factorization useful for simplifying expressions or solving equations. **Final answer:** $$x^3 - b^3 = (x - b)(x^2 + xb + b^2)$$