I’ve spent a ridiculous amount of time agonising over the reason hive stems exist, given that they’re full of hexagons (some full?) and seem to only have living space attached to the outsides;

But when you consider Sollux’ world as a macrocosm of the beehouses inside his hive, a lot of possibilities present themselves.
The first, most fanwanky idea that springs to mind is that the stem is somehow involved in the production of sopor slime; an important substance in troll society that helps (them) not be such complete idiot(s) all the time. But the fact that Sollux doesn’t really seem like he’s doing any actual work there doesn’t exactly credit the idea very much - all the trolls living there can only be kids, anyway, so any actual production probably doesn’t actually happen on the homeworld like this.
More likely the whole thing is probably just a really, really big computer, and the green shit in the hexagonal columns is the same sort of data slime that leaks from a game grub. Hey, maybe there’s actually some big data maggots down there somewhere. That’s what hive cells are for, right?
Sollux probably has some big government surveillance equipment churning and gurgling away right underneath his residence and has no idea. His hacking could just be doing work for them. The irony grub doesn’t stop from leaking.