What do you use to connect simple battery holders?
Great googly moogly! That's a lot of AA batteries ... as other commenters have mentioned, that's a pretty cumbersome solution for power. A lead acid or even LIPO (if you have the necessary charging station for them) would work.

If you want to go through with your particular design (If you give more information on what you're try to acheive, I or others may be able to give different options), then yes, soldering the wires together would be the way to go. A hot glue gun is a pretty handy tool too for mounting your cases to ... whatever it is you're doing, if it doesn't need to be super rugged.