[vikingerik]

If what's fun is the reasoning, then the thing to do is other shapes and styles of puzzles besides the cube.

This is my collection: https://imgur.com/v9OuYNw

Like you, I learned the 3x3x3 in high school via memorized algorithms, and that was only so interesting. Years later my brother got me a Megaminx (the dodecahedron equivalent to the 3x3x3 cube, third one in the top row there) and I was absolutely fascinated by learning to solve that by porting what I knew from the cube. From there I got all those other shapes as well. The most interesting ones to search by name: Dayan Gem 3 (the one that looks like the Star of David), Face-Turning Octahedron (last one in the second row), Helicopter Cube (to the right of the 3x3x4), Rex Cube (right from the Helicopter Cube).