Question 1099103
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The big cube has 8 corners.
The {{{highlight(8)}}} little cubes on those corners will have 3 faces painted.
 

The big cube has 12 edges.
There are 6 little cubes along each of those edges,
but the 2 at the ends are on a corner of the big cube.
We already figured out what happens with those little cubes.
The little cubes on the big cube's edges that are not on a corner
will have 2 faces painted.
There are 6-2=4 such little cubes on each of the 12 edges,
for a total of {{{4*12=highlight(48)}}} little cubes with 2 faces painted.
 
There are also {{{4*4=16}}} little cubes forming the center of each big  cube face
that will have only one face painted. You did not ask about those, but there are
{{{6*16=96}}} with exactly one face painted.
 
If you peel the outer layer of little cubes, you get a medium sized cube,
with 4 cm edges made up of {{{4*4*4=64}}} little cubes.
Those {{{highlight(64)}}} little cubes have no face painted.
 
VERIFICATION:
aiming up the numbers of little cubes with exactly 0, 1, 2, and 3 faces painted we get
{{{64+96+48+8=216}}} and that makes sense,
because a big cube with 6 cm edges is made up of {{{6*6*6=216}}}
little cubes with 1 cm edges.