You can try to solve it, but only if you are a crossword aficionado.
From a more theoretical point of view, it is just one of many our computer algorithm has found so far. There are about 10^400 possible 8*8*8 cubes with valid words in one direction, from the same dictionary of about 300 000 English words. Only a tiny minority,of those cubes,maybe a googol or less, are consistent crosswords in 3D, which means that the other two directions are also filed with regular words.
Perhaps the dictionary should be reduced, perhaps it should be broaden. Perhaps an application should be written, perhaps the paper lowtech version is the best. Maybe both. Perhaps a smaller cube 7*7*7 with only 7 letters long words would be fine?
Of course, the computer algorithm, with a working name WoShi is good for other tasks as well. Mainly for scheduling. But never the less, this crosswording might be an interesting niche, that is still an open question.