To solve the equation 3x - 1^3 = -27, we need to simplify the equation and isolate the variable x.

First, let's simplify the equation by evaluating 1^3, which is equal to 1:

3x - 1 = -27

Next, let's isolate the variable x by adding 1 to both sides of the equation:

3x = -27 + 1
3x = -26

Finally, divide both sides of the equation by 3 to solve for x:

x = -26/3

Therefore, the solution to the equation 3x - 1^3 = -27 is x = -26/3.