A video on YouTube or such of the first row of cubes printing would be immensely helpful.
Check all the connections on your z-axis. Loose couplers, misaligned gantry, bent screws, plastic or dirt in the z-screws, steppers not aligned in the frame, loose frame or gantry screws could all cause motion to have backlash or bind at the bottom of the z-axis and then loosen up once the z-gantry gets a few millimeters up the shaft.
Printing PLA with ABS bed and nozzle temperatures, or using the wrong surface could also cause such problems.