1. **State the problem:** Simplify the expression $$(a + 8)(a^2 - 8a + 64)$$. 2. **Recall the formula:** This expression resembles the product of a binomial and a trinomial that can be recognized as a sum of cubes formula: $$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$$. 3. **Identify terms:** Here, $x = a$ and $y = 8$. 4. **Apply the sum of cubes formula:** $$ (a + 8)(a^2 - 8a + 64) = a^3 + 8^3 $$ 5. **Calculate the cube:** $$8^3 = 512 $$ 6. **Final simplified expression:** $$a^3 + 512$$ This is the simplified form of the given expression using the sum of cubes identity.