I had a fabulous, very big begonia tuber that I called "Big Daddy". I went to a talk on growing begonias where the expert said that you could divide very big tubers. I did it, but it was never the same. :-)
The moral is, you may be able to, but it's probably better left alone. It probably wouldn't bloom nearly as wonderfully.

Just leave it be, Incapability, and enjoy the flowers next year. Is this a pot plant or a garden plant? If the latter, can you not collect seed and grow them on?

I have never heard of splitting a cyclamen corm. Some of ours are pretty large but I wouldn't consider doing anything to them.