The Black Pudding has a slam attack that deals (2d6+4 plus 2d6 acid) damage with each hit. It also has listed under special attacks "constrict 2d6+4 plus 2d6 acid." It has the Constrict and Improved Grab special attacks.
In the description under the Black Pudding we see this:
Constrict (Ex): A black pudding deals automatic slam and acid damage with a successful grapple check. The opponent’s clothing and armor take a -4 penalty on Reflex saves against the acid.
This seems an odd way of noting the constriction damage, that it deals "automatic slam and acid damage" with a successful grapple check. It already would deal that damage with a successful grapple check by virtue of having Improved Grab:
...
A successful hold does not deal any extra damage unless the creature also has the constrict special attack. If the creature does not constrict, each successful grapple check it makes during successive rounds automatically deals the damage indicated for the attack that established the hold. Otherwise, it deals constriction damage as well (the amount is given in the creature’s descriptive text).
Also, from Constrict:
A creature with this special attack can crush an opponent, dealing bludgeoning damage, after making a successful grapple check. The amount of damage is given in the creature’s entry. If the creature also has the improved grab ability it deals constriction damage in addition to damage dealt by the weapon used to grab.
So, despite the odd wording under the Black Pudding's stat block, it does deal 4d6+8 plus 4d6 acid with each successful grapple check, correct?
I guess technically it should still be two separate instances of damage (important for DR and energy resistance purposes), but that aside, its total damage dealt will still be what I listed above.