I have a mystery that's out of the ordinary.
If you visit http://www.trump.de/magic-squares/magic-cubes and check the History of Perfect Magic Cubes, you will see that a 7th-order perfect magic cube was discovered by Andrew H. Frost back in 1866 (before there were electronic computers) while 5th- and 6th-order perfect magic cubes were discovered by Walter Trump in 2003.
The 7th-order cube consists of 343 numbers while the 5th- and 6th-order cubes consist of 125 and 216 numbers respectively. It amazes me that the biggest cube was discovered way ahead of the other two smaller ones (and without a computer).
I would think that Mr. Frost must have found a shortcut to that 7th-order perfect cube. So far I haven't found an explanation as to how Mr. Frost did it and was wondering if someone can furnish any details?