puzzle 3-d visualization

Question

729 small cube are painted pink on each face and then arranged to form 27 identical middle-size cubes.Each middle size cube is painted black and then arranged together to form one large cube. And this large cube is painted pink again.What is the number of small cubes that have atleast one side black. I am not able to visualize this problem pls help

Answer 1

The painting of the $27$ middle-sized cubes produces $27\cdot8$ small cubes with a black corner, $27\cdot12$ small cubes with a black edge and $27\cdot6$ small cubes with a black face (and leaves $27$ small cubes in the centres all pink).

The painting of the big cube destroys $8$ corners. Along each of the $12$ edges of the big cube, there are $3$ small cubes that had only that edge black, so $12\cdot3=36$ edges are destroyed. And on each of the $6$ faces of the big cube, there are $9$ small cubes that had only that face black, so $6\cdot9=54$ faces are destroyed.

That leaves $(27-1)\cdot8=208$ (former) corners, $(27-3)\cdot12=288$ (former) edges and $(27-9)\cdot6=108$ faces, for a total of $208+288+108=604$ small cubes that still have some black.

Answer 2

The number of cubes with at least one black face is $9^3 - 5^3 = 604$.

Following picture is a visual illustration of the configuration of cubes.
Cubes with at least one black face has been make partially transparent.
As one can see, there are $(2 + 1 + 2)^3 = 5^3$ cubes whose faces are all pink.