If total number of pieces (Smaller cubes/cuboids) is 45 then find the possible number of cuts.

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 total number of cut is 10 then for maximum number of pieces these cuts have to be well distributed in three planes. For 10 cuts, 3,3 and 4 is the distribution of cuts.
Hence total number of pieces is
(3 + 3)(3 + 1)(4 + 1) = 4 x 4 5 = 80

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 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

Since total number of cubes is hence in the formula we will substitute n = 6
Number of the cubes with 2 faces painted is 6(6 - 2)²
= 6 x 16 = 96

Since total number of cubes is hence in the formula we will substitute n = 6
At most 2 faces painted means number of cubes with 0 face painted + number of cubes with 1 face painted + number of cubes with 2 face painted = 64 + 48 + 96 = 208