Inspired by my little cousin - the greatest artist of all time
One of the dreams of my little cousin is to become a great architect. His parents have given him many unit cube blocks to hone his skills.
One time, I noticed that he built 2 distinct square-based cuboids, in which exactly half of the cubes used could be seen from the outside.
What is the total number of cubes that he used?
Note: Cubes that are touching the ground, but not on the outside, canot be side. As an explicit example, the smallest building that hides at least 1 cube, has a square base of 3, and a height of 2. Exactly 1 cube not visible.
Special thanks to: Michael Mendrin