I think the parent poster means a "cube of air" as in a region of air, not something bounded on all 6 sides by glass walls. But to your question, if it was a g

I think the parent poster means a "cube of air" as in a region of air, not something bounded on all 6 sides by glass walls. But to your question, if it was a glass cube, I'm pretty sure the drone would hover in the middle of the cube while gravity pulls it down exactly like if the drone was turned off, based on conservation of momentum. Sure the drone is pushing the air down, but then the air hits the bottom, bounces up to the top, and then gets pushed by the drone again. It's (very literally) a closed system, so nothing happening inside is really noticeable outside, and vice-versa (steady state, if you smack the box the drone will notice).