I believe you are referring to Staff of the Arcanum, which has Mana Drain 1 for both attacks. I believe the exclusion of the '+' is a misprint, and it should say Mana Drain +1.
Mana Drain +X
If this attack damages an enemy creature, that creature's controller loses X mana from this mana supply (if he has any). If the attack makes multiple attacks against the same or different objects, it gains this bonus only for the first attack it makes.
So in the case of the staff your opponent mage would lose 1 mana, if your dice get past any armor his creature may have and do at least 1 damage to the creature. The same is true with the Mana Leech, however, since its full attack is Mana Drain +2, then your opponent mage would lose 2 mana. Mana Drain does not allow you to roll any extra dice, it simply says how much mana your opponent mage loses if you damage your creature target.
I'm not sure if there's a reason that Mana Drain +X starts by saying the attack must be against a creature for the attack to work, but then at the end seems to indicate that it could work against any object, I'm assuming this is a misprint as well. When I have played we went with that the effect only ever works against creatures and not any other kind of object.