By inspection, you can show that 4 is a root.
Divide x3 - 64 by x - 4 ---> the quotient is x2 + 4x + 16.
Use the quadratic formula on the quotient to get the two answers: -2 +/- 2·i·sqrt(3).
The three solutions are: 4, -2 + 2·i·sqrt(3), -2 - 2·i·sqrt(3).