how do you factor 4x^3-108
in the first you indicate the sum, in the second you indicate a difference (minus). Since they are similar, we'll address both.
For the first, this also looks like the sum of two cubes (a3 + b3) = (a + b) (a2 - ab + b2). But 4 isn't a perfect cube, and neither is 108. BUT... if we factor out a 4, we get
4(x3 + 27) = 4 (x + 3)(x2 - 3x + 9)
For the second, we approach it the same way, except our signs change:
Difference of two cubes (a3 - b3) = (a - b) (a2 + ab + b2).
4(x3 - 27) = 4 (x - 3)(x2 - 3x + 9)