{Delif's Cube} says, "Remove a cube counter to regenerate target creature."
If i regenerate my own creature it comes back under my control right? However what happens if i use {Delif's Cube} and regenerate my opponents creature. Does he get it or do i?
Regeneration prevents a creature from dying. It doesn't bring it back from the dead. It never goes to the graveyard.
You can regenerate any creature you can target, but keeping your enemies creatures from being destroyed is usually not a good game plan.