The six faces of a cube are painted in a manner that no two adjacent faces have the same colour. The three colour used in the painting are red, blue and green. The cube is then cut into 64 equal cubical parts. Answer the following question.
How many cubes in all have three sides painted?

(a)?24

(b)?16

(c)?10

(d)?8

Dear Student,
The answer is Option D (8).
Reason: A cube is painted and then cut into 64 equal pieces ( 3 vertical cuts and 3 horizontal cuts). Now, the cubes having vertices of the original cube will have 3 sides painted. 
Therefore, 4 corners on the top and 4 corners on the bottom will form cubes such that those 8cubes will have 3 sides painted. 
Kindly note that Volume of bigger cube = 64× volume of each smaller cube
$$\begin{gathered} S^3= 64s^3 \\ {S}^3={\left(4s\right)}^3 \\ S= 4s \end{gathered}$$
So, side of the bigger cube = 4× side of each smaller cube.
Hope this help you! 
Regards