4.

The cube root of a number x means "What number multiplied by itself three times is equal to x?"

In this case "x" is 64, which happens to be a power of 2. 2 * 2 = 4, 4 * 2 = 8 => (2 * 2 * 2) = 8 and 8 * 8 = 64 => (2 * 2 * 2) * (2 * 2 * 2) = 64. Note that the only thing we've done here is arrange the 2 multiplication so it looks like 8 * 8.

We can also arrange the same multiplication as so: (2 * 2) * (2 * 2) * (2 * 2) = 64. This is a representation that has three sets of parentheses with identical multiplication, which is the same as saying a number multiplied by itself three times.

So (2 * 2) * (2 * 2) * (2 * 2) = 64 also means 4 * 4 * 4 = 64, so I hope you're convinced that the cube root of 64 is 4.