To solve the equation \( x^3 = -8 \), we can take the cube root of both sides.
\[ x = \sqrt[3]{-8} \]
Since \(-8\) can be expressed as \(-2^3\), we have:
\[ x = -2 \]
Thus, the solution to the equation \( x^3 = -8 \) is:
\[ x = -2 \]
This is the only real solution, as the cube function is one-to-one.