The original order-3 Rubik's cube with 6 different colors is probably too difficult for most people to independently come up with a solving strategy, so they resort to the mundane task of looking up and memorizing algorithms.
Better would be simpler puzzles, which after playing with for a while, one can achieve deep understanding of the cube: become able to mentally manipulate and explore, have a practical understanding of group theory.
2x2 cube with several faces the same color. An order 2 cube can be simulated on an order 3 by having the middle slices all the same color.
Rather than many separate cubes of varying initial patterns, the most practical way would probably be a cube for which the "stickers" can be easily and repeatedly removed and reattached. Perhaps tiles, with magnets or mechanical clips. Not a child's toy: the many small parts will be a hazard. Being able to remove and replace provides an easy way to solve the cube if you scramble it beyond your current ability to solve it.
Perhaps have two cubes so as not to have to visualize the goal. The other does not need to twist. This one can store the spare tiles.
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