In the expressions certains d'entre eux, aucun d'entre eux, etc., is there an explanation why there is a "de"? The meaning seems to be just "some of them" and "none of them", so I'm not sure why it is necessary to place a "de" in front of the preposition.
As underlined @oldergod, without "de" those expressions would not have the same meaning :
- certains / aucun = some / none
- de = of
- entre = between
- eux = them
So without "de" you have no link between the quantity (some/none) and the fact that this quantity is taken inside the group (of them).
You would be understood because it is not a big word missing, but it will appear as strange and incorrect - you will probably be corrected.