Have you tried doing the "tally" method? I have found this to be by far the best way to approach cube counting and save a lot of time.
On your sheet write
0
1
2
3
4
5
And go through the whole figure once. Every time you see a cube of that side, say a 3 sided, put a hash mark down next to the 3. That way you only have to go through the cube one time for 3-5 questions and it makes it go by much quicker.