1. **State the problem:** Solve the equation $x^3 - 8 = 0$ for $x$. 2. **Formula and rules:** This is a cubic equation. We can isolate $x^3$ and then take the cube root of both sides. 3. **Isolate $x^3$:** $$x^3 = 8$$ 4. **Take the cube root:** $$x = \sqrt[3]{8}$$ 5. **Evaluate the cube root:** Since $8 = 2^3$, we have $$x = 2$$ 6. **Final answer:** $$\boxed{2}$$ The solution to the equation $x^3 - 8 = 0$ is $x = 2$.