To find the cube root of 512, we can express it mathematically as:
\[ \sqrt[3]{512} \]
Calculating this, we find that:
\[ 8 \times 8 \times 8 = 512 \]
Thus, the cube root of 512 is:
\[ \sqrt[3]{512} = 8 \]
While negative numbers can also be cube roots, since \(-8 \times -8 \times -8 = -512\), they don't apply in this case where we're seeking the cube root of a positive number.
Therefore, the answer is:
\[ 8 \]