To solve the equation (2x - 1)^3 = 27, we need to find the value of x.

First, we can take the cube root of both sides of the equation to eliminate the exponent:

∛((2x - 1)^3) = ∛27

Simplifying the cube root of 27 gives us:

2x - 1 = 3

Next, we can isolate the variable x by adding 1 to both sides of the equation:

2x = 3 + 1

2x = 4

Finally, we divide both sides of the equation by 2 to solve for x:

x = 4/2

x = 2

Therefore, the solution to the equation (2x - 1)^3 = 27 is x = 2.