The intention is for you to use the 8x8 version of Phistomefel’s theorem. Which, as far as I know, is a novel concept. If you can do that, this puzzle is much simpler. However, it is possible to solve this puzzle without the theorem. Here is an explanation image:
There are two version of Phistomefel’s theorem that show up in this puzzle with non-square regions. In both sides of this image, the red and blue highlighted squares contain the same digits (red=blue). The proof for this follows from the original discovery. If you don’t know what I’m talking about, see here. Rules:
-Ordinary sudoku rules apply.
-Killer Sudoku Rules apply. Digits cannot repeat in cages and must sum to the number in the top left (if given).