To solve this equation, we can expand both sides and then simplify:

Expanding the left side:
(2x - 1)^3 = (2x - 1)(2x - 1)(2x - 1)
= (4x^2 - 4x + 1)(2x - 1)
= 8x^3 - 8x^2 + 2x - 4x^2 + 4x - 1
= 8x^3 - 12x^2 + 6x - 1

Expanding the right side:
(3x)^3 = 27x^3

Now we have the equation:
8x^3 - 12x^2 + 6x - 1 = 27x^3

Combining like terms:
8x^3 - 27x^3 - 12x^2 + 6x - 1 = 0
-19x^3 - 12x^2 + 6x - 1 = 0

This is a cubic equation, and it may not have a simple solution. We can use numerical methods or a graphing calculator to find the approximate solutions.