Imagine a large cube made of 10 small cubes in height, width and depth (i.e. 10x10x10)...

No, it's not 9&3.
It's 8&3.

Try to picture the cube; for instance, think about this problem with a cube made of 2 little cube in heigth etc...
there's not one cube in the middle that you can't see, you see them all.
3 cubes = 1 cube you can't see
4 cubes = 4 cubes you can't see
etc...

"The easy answer is to think of it in terms of volume, i.e. total volume is 10&3 =1000 and you strip out the middle of the cube which is 8&3=512, which gives you the same answer of 488."

shouldnt the middle of the cube be 9&3 and not 8&3- giving an answer of 10&3-9&3= 271.

my answer would be as follows, but then again, i might be retarded.

inside the 10x10x10 cube, one cannot see 9x9x9 cubes. so, one can see10x10x10-9x9x9=271 cubes

If the line of sight is along the line perpendicular to a surface and in its centre, you'll see 100.

If the line of sight is at one of the corners, it will be
(sum of the 3 surface areas without the edges +
sum of the 3 edges without the common corner +
the corner)
= (9&2 x 3) + (9 x 3) + 1
= 243 + 27 + 1
= 271.

depends on whether the cubes are made of opaque or transparent material. my answer would be - you wouldnt be able to see any of the small cubes no matter what angle you look from!