First, let's simplify the expression:

(6x^3 - 1)^2 = (6x^3 - 1)(6x^3 - 1) = 36x^6 - 6x^3 - 6x^3 + 1 = 36x^6 - 12x^3 + 1

(4x^3 - 1)(9x^3 - 4) = 36x^6 - 16x^3 - 9x^3 + 4 = 36x^6 - 25x^3 + 4

Now, substitute back into the original expression:

36x^6 - 12x^3 + 1 - (36x^6 - 25x^3 + 4) = 36x^6 - 12x^3 + 1 - 36x^6 + 25x^3 - 4
= 13x^3 - 3

Therefore, the simplified expression is 13x^3 - 3.