I observed that if I remove one (or all 8) piece(s) in the corners, and only them without adjacent ones, the total area does not change.
I consider the surface area of a small square as a unit of surface.
First class of solutions:
I removed all eight corners, leaving the total area unchanged.
I removed the central cube of the top surface obtaining an increase of the surface area with four units.
I removed one cube from the middle of an edge at the top (any of the four remaining) and I arrived at a figure with ten cubes less then the original one but with the same surface area.
(There's a lot more solutions here: https://nrich.maths.org/787/solution)
