Before you start counting and tallying, take 5 seconds or so to look at the cube structure as a whole to investigate the overlapped areas and get a better feel for what's hidden or what's touching other non consecutive cubes.
By not immediately consecutive cubes I'm taking about the 4-cube underneath that 5-sided cube that at first glance one might think it has only 3-sides painted. Other than that I'd just familiarize yourself with patterns to help you count faster, i.e. a "tower" would have 2 4-sided cubes and a 5-sided cube on top. If you can recognize this quickly then when you take your eyes off the monitor you can mark multiple cubes at a time rather than going one at a time.
Just keep practicing cube counting, because at least for me, during the actual exam, cube counting allowed me to play "catch up" with my pace/timing by completing it in ~8 minutes.
