1. **State the problem:** Factor the expression $$x^3 - 64$$ completely. 2. **Recognize the formula:** This is a difference of cubes since $$64 = 4^3$$. The difference of cubes formula is: $$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$ 3. **Identify values:** Here, $$a = x$$ and $$b = 4$$. 4. **Apply the formula:** $$x^3 - 64 = (x - 4)(x^2 + 4x + 16)$$ 5. **Check for further factorization:** The quadratic $$x^2 + 4x + 16$$ does not factor further over the real numbers because its discriminant $$\Delta = 4^2 - 4 \times 1 \times 16 = 16 - 64 = -48 < 0$$. 6. **Final answer:** $$\boxed{(x - 4)(x^2 + 4x + 16)}$$