Just search "STEM toys", and that should get you started. Using this page which lists
journal search engines, I just used
Google Scholar and the first search result's abstract seems to be along the lines of what you're looking for. (The "You Can Do the Rubik's Cube" program has integrated the Rubik's cube into education.) But one guy made a video saying that high school maths should be optional to students, not required. He proposed to integrate puzzle solving as a logical substitute.
Video.
So all of this is aimed at the benefit of education. If you were looking for early childhood brain development,
the possibility of the Rubik's cube to inspire new maths, etc., then search for it and see what you find.
But the majority of people only see the cube as a toy.
But for puzzles in general, if you aim to solve them in fewer moves/steps, that could prepare one mentally to be a supply chain analyst, industrial engineer, software developer, etc.
Also, in computational complexity,
solving the nxnxn Rubik's cube optimally is classified as "NP-Complete" by computer scientists. That basically means that there are different types of problems, puzzles, games, etc., which are of a certain complexity. And if a group of problems, puzzles, games, etc., are all of the same complexity then, if you can learn how to solve any one of them more efficiently than what they are classified as, then you can actually learn to solve them all more efficiently. Given that the Rubik's cube is a more visual/concrete object to experiment with rather than most things, if someone wants to prove that solving the Rubik's cube optimally isn't as complex as is currently believed, a lot of real-world problems could be resolved more efficiently on a daily basis.
So the point of this paragraph is that you could look up journals talking about computational complexity, as they are technically related to the Rubik's cube.
