1. **State the problem:** We need to find the value of $m$ such that $$x^3 - 8 + m = (x + 1)(x^2 - x + 1).$$ 2. **Recall the formula:** The right side is a product of a binomial and a trinomial. We will expand it using distributive property: $$ (x + 1)(x^2 - x + 1) = x(x^2 - x + 1) + 1(x^2 - x + 1). $$ 3. **Expand the right side:** $$ x^3 - x^2 + x + x^2 - x + 1 = x^3 + 1. $$ 4. **Simplify the right side:** The terms $-x^2$ and $+x^2$ cancel out, and $+x$ and $-x$ cancel out, leaving: $$ x^3 + 1. $$ 5. **Set the expressions equal:** $$ x^3 - 8 + m = x^3 + 1. $$ 6. **Solve for $m$:** Subtract $x^3$ from both sides: $$ -8 + m = 1. $$ Add 8 to both sides: $$ m = 1 + 8 = 9. $$ **Final answer:** $m = 9$ which corresponds to option (c).