As previously noted, this page (which is a descendant of this page, not having backward links on it) notes that of twelve possible puzzles that can be formed from the Mikusiński cube by mirror reflections of one or more pieces, only one of them has no solution in the form of a 3 by 3 by 3 cube, and all the rest have only a small number of possible solutions, thus presumably making them difficult puzzles.
The puzzles are noted as having been supplied by Knowledge for Use, which appears to be the entity with this web site.
Here is a diagram showing the twelve possible variations on the Mikusiński cube which that site discusses, together with one solution for each of the variations which has a solution:
