If total number of cuts is 10 then find the maximum number of pieces that can be obtained.

If total number of cuts is 10 then minimum number of pieces is 11 when cut is made in one plane only.

For maximum number of pieces cuts has to be 6, 7 and 7 and maximum number of pieces is (6 + 1)(7 + 1)(7 + 1) = 7 x 8 x 8 = 448.
Minimum number of pieces is 20 + 1 = 21.
Hence required ratio is 448:21

If 45 = 1 x 1 x 45 then we require only 44 cuts in one plane.
If 1 x 3 x 15 then we require 2 cuts in one plane and 14 cuts in other plane so total number of cuts is 2 + 14 = 16.
If 1 x 5 x 9 the we require 4 cuts in one plane and 8 cuts in other plane so total number of cuts is 4 + 8 = 12
If 3 x 3 x 5 then we require 2 cuts in one plane, 2 cuts in 2^nd plane and 4 cuts in 3^rd plane so total number of cuts is 2 + 2 + 4 = 8.

For maximum number of cuts it has to be in one cut only, so number of cuts is 49

For minimum number of cuts we will get 50 from 2 x 5 x 5 and cuts is 1 + 4 + 4 = 9

Since total number of cubes is hence in the formula we will substitute n = 6
Number of the cubes with 0 faces painted is (6 - 2)³ = 4³ = 64