The given equation is:

$x^3 = 512$

To solve for $x$, we take the cube root of both sides:

$x = \sqrt[3]{512}$

Since $512 = 8^3$, the cube root of $512$ is 8:

$x = 8$

Thus, the real solution is:

$x = 8$

Would you like a detailed explanation of how cube roots work?

Here are 5 related questions for you to consider:

1. How would you solve $x^3 = -512$?
2. What is the cube root of $1000$?
3. What are the real solutions to $x^3 = 27$?
4. How would you solve $x^4 = 16$?
5. Can a cubic equation have more than one real solution?

Tip: When solving equations involving cubes, remember that cube roots of positive numbers are positive, while cube roots of negative numbers are negative.