To find the cube root of 512, we can express it as:
\[ \sqrt[3]{512} \]
Now, we can factor 512 to see if it is a perfect cube:
\[ 512 = 2^9 \]
Since \(2^9\) can be rewritten in terms of cubes:
\[ 512 = (2^3)^3 = 8^3 \]
Thus,
\[ \sqrt[3]{512} = 8. \]
Therefore, the cube root of 512 is \(8\).