if you just want to kill them, just dump the cages in a magma pit with an internal atom smasher (dump them in, pull the lever), using wooden cages. Your carpenter won't be happy about seeing his crap get smashed, but he can live with it. certain monsters cannot be pitted reliably, notably most thief types. the goblins should always be disarmed first (dump all clothing and weapons in the stocks screen that you didn't make yourself). If there's already something "scary" in the pit, and you don't have the pit covered with a hatch, it'll scare your dwarves and thus free whatever creature they were trying to pit.
If you want them to have an arena deathmatch, then use something that WILL kill the goblins, such as a forgotten beast, preferably without wings and without a syndrome breath weapon. Consider placing a room off of your cavern entrance containing nothing but a stone or wooden door, past your traps. The back of the room is a raised bridge blocking a path to the arena, and there is another bridge to close off the room from the hallway. When you wish DEATH to happen, release the FB by lowering the REAR bridge, and when you wish to put the forgotten beast back in the room, close it into the ARENA, build a wooden door inside the holding cell again, close off the room from the main hallway, and then let the FB back into it's room. It'll stay by the door long enough to trash it, at which point you close it in completely. I do this to deal with unwanted immigrants and nobles and children. Otherwise, see if you can trap a giant cave spider, and use noexotics (you don't need to regen if you apply it to your save file's raws as well, but it's a one-way conversion), because then you can apply silk webs to your trap hallway.
In the end, pits are NOT a reliable way to free monsters. It's easier just to link cages up, and then release them that way once they are properly sequestered.