Do cartridge BB's have both ends removeable?
Most of the standard square taper bottom brackets on the market (e.g. Shimano BB-UN54/BB-UN55) have one cup permanently attached to the bottom bracket (usually drive side) and the other one removable.

However, some manufacturers make ones with both sides removable (e.g. Phil Wood) and some other variations on installation (notably threadless ones like the Velo Orange Grand Cru Universal).