Carpentry and Woodworking - Custom built storage unit won't stay square

Hello,
I've built two small storage units for my sons room. I used MDF 5/8" thick to build it. The first unit is 4 cubes (roughly 12"x12" per cube - two upper and two lower), the second unit is 2 cubes (same size - stacked vertically) I plan to paint them with a white melamine to match some IKEA furniture he already has.

I used a pocket jig to drill holes and hide the screws, and I left the back of the units open. They were square, when glued and screwed into place, but when I stand it up.. it leans ever so slightly to the right and knocks the entire unit out of square. I'm certain there are a thousand things that I didn't do "right" while building these units, but they are done now and I'm wondering if there is anything that I can do to bring them back to square.

If there is any carpentry classification before beginner.. that would be me. Any suggestions would be appreciated.

Thanks.

Is the floor level? Does it do the same thing in another room? If it's the unit itself, I would look for some brackets to stop it from shifting.

have you checked the outside with a square if they are square check the floor for level, if they aren't square you might be able to run a wire from corner to corner to pull it back square on the back side.

Murphy was an optimist.

Not installing a back or corner bracing sufficient to keep it stable is the culprit. With children, it is best to install a rail under the top board, attached to the top and sides, then attach it to the wall. You don't want them pulling it down on themselves. That will keep it square and upright at the same time.

Thank you to everyone for taking the time to offer suggestions. I will put backs on them and hopefully this will do the trick.

Thanks again.

When installing woodscrews in the edge of manufactured materials like MDF, it's all too easy to split the sides of a workpiece — even if you drill a pilot hole first. To prevent this, I support the sides by clamping an ordinary handscrew clamp across the workpiece. Even doing this initially won't always give a long-term solid joint due to the nature of MDF. It may be necessary to add a back to ensure the necessary stability.