Another way of solving this
Since the volume is 64 so the side must be 4 units each
The total no. of unit cubes to "coat" the bigger cube would be as
4^2=16 cubes to cover each face so 16*6=96
4 cubes on each edge so 4*12 = 48
one at each corner so 8
All add up to 96+48+8=152
Hi! I did not understand why you did 4^2, and why 8 more cubes are required at the corners.
The 4^ 2 is because there are 4 cubes on one side of the face. A face has 4 sides ( which makes it a square), so one face has 4+4+4+4 = 16 cubes.
Then, there are 6 faces, so 16*6 = 96 cubes
There are also 4 cubes on each edge = 4*12= 48
and since there are 8 corners in a big cube ( 4 that you can see, 4 at the back, and one at the bottom that you cant see). If you draw a cube and try counting the edges you'll find 8 edges
Kudos if I helped