The following figure shows the cubes painted blue on all faces and divided into 125 smaller cubes:

The figure may be analysed by dividing it into five horizontal layers:

In layer 1 : the nine central cubes have  only one face painted, four cubes at the corner have three faces painted and the remaining 12 cubes have two faces painted. 

In each of the layers II, III, and IV : the nine central cubes have no face painted, the four cubes at the corner have two faces painted and the remaining 12 cubes have one face painted.

In layer V : the 9 central cubes have only one face painted, four cubes at the corner have three faces painted and the remaining 12 cubes have two faces painted.

(2) There are 9 cubes in each of the layers I and V and there are 12 cubes in each of the layers II, III and IV which are painted on one face only.

Thus, there are such cubes.

Hence the correct option is D.

In the above question, the cube is given :

Clearly, 16 columns of 4 cubes each, are formed , by cutting the cube of 8 cm side into cubes of 2 cm side. To analyse the figure, four horizontal layers of 16 cubes each, are studied separately.

In layer I : four central cubes have only one face painted red, four cubes at the corners have three faces painted - red, blue and black . Out of the remaining  8 cubes , four cubes have two faces painted - red and black and four cubes have two faces painted - red and blue.

In layer II : four central  cubes have no face painted, four cubes at the corners have two faces painted - blue and black. Out of the remaining 8 cubes - four cubes have only one face painted - blue  and four cubes have only one face painted - black.

In layer III : four central cubes have no face painted, four cubes at the corners have two faces painted - blue  and blck. Out of the remaining 8 cubes - four cubes have only one  face painted - blue and four cubes have only one face painted - black.

In layer IV : four central cubes have only one face painted - reed, four cubes at the corners have three faces painted - red, blue and black. Out of the remaining 8 cubes - four cubes have two faces painted - red and black and four cubes have two faces painted - red and blue.

Thus Four central cubes in layer II and four central cubes in layer III have no face painted. Thus, there are 8 such cubes.

Hence the correct option is C.

In the above question, there is a cube given below :

Clearly, 16 columns of 4 cubes each, are formed , by cutting the cube of 8 cm side into cubes of 2 cm side. To analyse the figure, four horizontal layers of 16 cubes each, are studied separately.

In layer I : four central cubes have only one face painted red, four cubes at the corners have three faces painted - red, blue and black . Out of the remaining  8 cubes , four cubes have two faces painted - red and black and four cubes have two faces painted - red and blue.

In layer II : four central  cubes have no face painted, four cubes at the corners have two faces painted - blue and black. Out of the remaining 8 cubes - four cubes have only one face painted - blue  and four cubes have only one face painted - black.

In layer III : four central cubes have no face painted, four cubes at the corners have two faces painted - blue  and black. Out of the remaining 8 cubes - four cubes have only one  face painted - blue and four cubes have only one face painted - black.

In layer IV : four central cubes have only one face painted - red, four cubes at the corners have three faces painted - red, blue and black. Out of the remaining 8 cubes - four cubes have two faces painted - red and black and four cubes have two faces painted - red and blue.

(b) There are four cubes in layer I and four cubes in layer IV which have only one face painted red and all other faces unpainted. Thus, there are 8 such cubes.

Hence the correct option is B.