1. **State the problem:** Find the real solution(s) of the equation $$8x^3 = 64$$. 2. **Write the formula and rules:** To solve for $x$, we want to isolate $x$ by dividing both sides by 8 and then taking the cube root. 3. **Divide both sides by 8:** $$\cancel{8}x^3 = \frac{64}{\cancel{8}}$$ $$x^3 = 8$$ 4. **Take the cube root of both sides:** $$x = \sqrt[3]{8}$$ 5. **Evaluate the cube root:** Since $2^3 = 8$, we have $$x = 2$$ 6. **Conclusion:** The real solution to the equation is $x = 2$.