'Cube maths' page says:'In this case, once the second from last corner piece is placed, the
last piece can have only one automatic orientation, so 6561 must be
divided by 37, which is 2187.'
It must be divided by 3, not by 3? or multiplied by 3? which is 2187 (instead of 3?).
Same later: 'So 6561 must be divided by 211, which is 2048. '
This should be '4096 must be divided by 2'
Also: 'However, unlike corner pieces, it is impossible to exchange just two
edge pieces, so once the third from last is placed, the remaining two
can have only one possible arrangement, which means this figure must be
divided by 2'
Word 'unlike' is not a good choice here. One cannot exchange just two
edge pieces or just two corner pieces. One can exchange two
edge pieces and two corner pieces. In 4*4*4 cube you can exchange just two
edge or two corner pieces.
Result is correct though.
8!*3^7*12!*2^11/2 = 43252003274489856000