Not if your game disc is not in that Xbox 360 or if the maps need to be downloaded to it.
I think what you want to know is do you need your own copy of the DLC Zombie Maps or if you can somehow use those that are on someone else's Xbox 360 while you are playing online with them and you can not. You need to have the map in your harddrive or on your game disc to play it.
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Not on the same xbox/ps3 no unfortunately.
No you can't the game is only for xbox indie games.
No, you can only get the classic zombie maps if you have harden or prestige editions of the game and unless the release a map pack with the originals (which they probably will) you can't get them at all Rezurrection DLC will include the 4 WAW maps Nacht der Untoten, Verrückt, Shi No Numa, & Der Riese along with 5 new maps including zombie map Moon
You can go multi player and look up zombie mod servers all of them have the zm_(mapname) maps so you can search by zombie in server name or zm_ in server map. Unless you have your own server that you run you cannot play zombie mod with bots.
The related link lists the 8 maps currently out for the Call of Duty World at War (1 + 3 in Map Packs) and Call of Duty Black Ops (3 + 1 in First Strike Map Pack). Only the Hardened or Prestige Edition of Call of Duty Black Ops for the PS3 or Xbox 360 can play seven ( 8 with First Strike Map Pack) of those Maps. Zombie Maps have had successful sales and therefore will continue to be released as they are developed. Expect the next release later this spring for Call of Duty Black Ops