1. The problem asks to find the cube root of 64, which means we want to find a number $x$ such that $$x^3 = 64.$$ 2. The cube root is denoted as $\sqrt[3]{64}$ and it is the inverse operation of cubing a number. 3. To solve, we look for a number $x$ where $$x^3 = 64.$$ 4. Since $4^3 = 4 \times 4 \times 4 = 64,$ we have $$\sqrt[3]{64} = 4.$$ 5. Therefore, the cube root of 64 is 4.