1. **State the problem:** Solve the equation $x^3 = 8$ for $x$. 2. **Formula and rules:** To solve for $x$ when given $x^3 = a$, use the cube root: $x = \sqrt[3]{a}$. 3. **Apply the formula:** Here, $a = 8$, so $x = \sqrt[3]{8}$. 4. **Evaluate the cube root:** Since $2^3 = 8$, we have $\sqrt[3]{8} = 2$. 5. **Final answer:** $x = 2$. This means the value of $x$ that satisfies $x^3 = 8$ is $2$.