Hello, prasum!

Have you ever heard of *punctuation*?

A cube is coloured red on two opposite faces, blue on two adjacent faces,

and yellow on two remaining faces.

It is then cut into two halves along a plane parallel to red faces.

One piece is cut into 4 equal cubes and other one into 32 equal cubes.

How many cubes will not have any face coloured?

I don't suppose you made a sketch . . .

Consider a 4-inch cube.

Color the top and bottom red.

Color the front and left face blue.

Color the right and back face yellow.

Bisect the cube horizontally.

. . Each half is a $\displaystyle 4\!\times\!4\!\times\!2$ block.

The top half is cut into four equal cubes; each is $\displaystyle 2\!\times\!2\!\times\!2$

. . *All* of them will have at least one painted face.

Code:

* - - - * - - - *
/ / /|
/ R / R / |
/ / / |
* - - - * - - - * Y *
/ / /| /
/ R / R / | /
/ / / |/
* - - - * - - - * Y *
| | | /
| B | B | /
| | |/
* - - - * - - - *

The bottom half is cut into 32 equal cubes; each is $\displaystyle 1\!\times\!1\!\times\!1$

. . The central 4 cubes in the top layer are paintless.

Code:

* - * - * - * - *
/ / / / /|
* - * - * - * - *Y*
/ / x / x / /|/|
* - * - * - * - *Y*Y*
/ / x / x / /|/|/
* - * - * - * - *Y*Y*
/ / / / /|/|/
* - * - * - * - *Y*Y*
| B | B | B | B |/|/
* - * - * - * - *Y*
| B | B | B | B |/
* - * - * - * - *