# cubes at depth = 0 : 0
# cubes at depth = 1 : 8
# cubes at depth = 2 : 56
# cubes at depth = 3 : 224
# cubes at depth = 4 : 824
# cubes at depth = 5 : 3320
# cubes at depth = 6 : 13400
# cubes at depth = 7 : 53672
# cubes at depth = 8 : 214400
# cubes at depth = 9 : 857840
# cubes at depth = 10 : 3431600
Boundary + Inner Volume + Outer Volume = Volume of Region:
 4.41804885864258E-0002 + 4.16666151802847E+0000 + 9.61315799333460E+0000 =
 1.38239999999495E+0001 = 1.38240000000000E+0001
Final result:
 4.166662 < Volume =  4.188790 < 4.210842