How many cubes with 3 facefacecoloured?

Each has Red faces on top layer = all edges cube = 2 + 2 + 2 + 2 = 8

Only two faces are coloured is when cubes are at the edges (baring the corner cubes)
If no cubes have been removed then on each edges we will get 3 cubes that has exactly 2 faces coloured, hence total number of such cubes = 12 x 3 = 36, because we have 12 edges.
Out of these 3 cubes are removed hence required number of cubes = 36 - 3 = 33

In any plane, leave 4 sides cube and select (3 x 3 x 3) inter section. But
the cubes 2 x 2 x 1 give 2 less cube because that part we are already removed.
No. of cubes = (3 x 3 x 3) - 2 = 25.

Total no. of cubes = 5³ = 125,
Some cubes from different corners are removed and the number removed cubes are 2, 3, 4 and 4.
Remaining number of small cubes:
= 125 - 2 - 3 - 4 - 4 = 125 - 13 = 112

For least number of cuts 120 = 4 x 5 x 6 i.e number of cuts must be 3, 4 and 5 in three planes in this case number of cubes on a face is either 6 x 5 = 30 or 6 x 4 = 24 or 4 x 5 = 20 cubes . And number of cuboids on an edge is 4 or 5 or 6
In this case we have to use red and green twice and same colour should be on opposite faces then required cube is given by 4 edges (but not corner), maximum number of cubes one edge is 6 - 2 = 4 so required number of cubes is 4 x 4 = 16

Initial total number of cubes = 343,
Number of cubes removed = 27
Smaller 27 cubes painted blue
Exposed faces of original big cube (3 faces with 9 cube on each face i.e total 27 cubes) painted with black
Since 7 corner (Vertices) of bigger cube is untouched hence they are painted with three faces.
Now consider the corner from where we have removed 3 x 3 x 3 cubes,
After removed 3 new corners of the bigger cube will be generated that will be painted with 3 faces and 8 corners from smaller cube of 3 x 3 x 3 painted with 3 faces.
So the such total number of such cubes is 7 + 3 + 8 = 18.

Initial total number of cubes = 343,
Number of cubes removed = 27
Smaller 27 cubes painted blue
Exposed faces of original big cube (3 faces with 9 cube on each face i.e total 27 cubes) painted with black
In original big cube number of faces with one colour is 3(6 -2)² = 48 (here we have considered only 3 untouched of big cube)
But here we have removed a cubes of the form of 3 x 3 x 3 and again put it back so out of three new exposed faces of big cube we will have 4 cubes in each face that is painted with one colour hence number of cubes from these three surfaces is 3 x 4 = 12
Now consider out of 3 x 3 x 3 cubes we will have 6 cubes (one in each face ) which are painted only one face.
Hence total number of cubes = 48 + 12 + 6 = 66

Initial total number of cubes = 343,
Number of cubes removed = 27
Smaller 27 cubes painted blue
Exposed faces of original big cube (3 faces with 9 cube on each face i.e total 27 cubes) painted with black
Without any changes number of cubes with no face colour is given by (6 - 2)³ = 64
Now because of removal of 3 x 3 x 3 cubes from one of the corner from each face that were not painted earlier got exposed and will get painted, so from 3 x 3 x 3 cubes 4 x 3 = 12 cubes got painted, and a similar number from 3 exposed faces of big cube got painted.
Total number of cubes with no face painted is 64 - 12 - 12 = 40

Initial total number of cubes = 343,
Number of cubes removed = 27
Smaller 27 cubes painted blue
Exposed faces of original big cube (3 faces with 9 cube on each face i.e total 27 cubes) painted with black
Out of 27 small cubes from 3 x 3 x 3, outer 26 cubes are 1st painted with blue and then it is kept back with original cube and painted with yellow so out of 26 cubes only 5 edges will give us cubes with both the colours and number of such cubes are 12

Initial total number of cubes = 343,
Number of cubes removed = 27
Smaller 27 cubes painted blue
Exposed faces of original big cube (3 faces with 9 cube on each face i.e total 27 cubes) painted with black
Out of 12 cubes in previous question there are 4 cubes with 2 faces yellow so number of cubes painted two faces only one with yellow and one with blue is 12 - 4 = 8