If total number of cuts is 20 then find the ratio of maximum and minimum of pieces that can be obtained.

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.

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

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