How can I factor 27x³ 64=0?

You need to memorize how to factor cube roots, i. e. x^3 - y^3 or x^3 + y^3.

You left a + or - sign out but:

Here you have the difference of 2 cubes.

Then (3x - 4) (9x^2 + 12x + 16)

or (3x + 4) (9x^2 - 12x + 16)