Of course you can, just not a very good one. Since you're limited to illusory "objects," it's going to be, like you suggested, pretty much the same as your "sheet with a [photorealistic] picture of an empty room" only you've got one sheet on each side of an illusory cube.
Such an illusion would be roughly comparable to things like the chalk artists who draw pictures of holes and other impressive things on the sidewalk. Extremely believable when viewed from the intended angle, but stepping too far to one side or another results in the parallax giving it away almost immediately. If using a spell that allows the illusion to be altered on an ongoing basis you might be able to track a person or small group and adjust it to continuously be what they expect to see, but it's not going to be an easy thing to do and will become close to impossible if they split up.
How successful this would be as a tactic will be highly dependent on placement. Near a wall would work OK as the parallax will be minimized. And the further away from the observer the harder it will be to spot. In a room with say polished obsidian walls and floors where there aren't any distinguishing characteristics for the eye to use to see the parallax it might even hold up to anything short of someone walking into it.
Do note two things though:
First, if I were the DM, I'd probably ask for a perception (or maybe stealth, I'd have to think about it) check to determine how clearly you can visualize exactly what texture needs to be on the cube to make it appear empty from a particular location. (Though I'd give you a big bonus if you took the time to scout it out and actually look at it from that location.) This isn't a normal "hey, there's a barrel here" use of an illusion spell, this illusion has to merge flawlessly with its environment, even moreso than putting an illusory wall over a doorway. If you don't line the bricks up with the background, or if you cut off half a wall sconce, it just got a lot more likely that somebody will notice. They won't be able to see through it until they realise it's illusory, but "Hey Thak! There's a weird piece of wall standing in the middle of the room!" is generally not something you'll be pleased to hear.
Second, consider whether you actually want your DM to think of doing this. This is the kind of trick that gives a much larger advantage to well-entrenched defenders than to wandering adventurers since the defenders will have had time to study and perfect the appearance of their illusion to match their intended purpose.
Other than that though, "Illusion of what this place would look like except without me in it as seen from over there" has been a staple part of more D&D campaigns than I can count. It gets past some of the weaknesses of Invisibility at the cost of being usable in a much more limited set of circumstances and being easier to pierce once the other guys realise what's going on.