Thread: Cube bookcase help

My preferred approach would be

Rout a trench on each of the shelves top and bottom 5mm deep, cut the vertical dividers to fit. Glue should be enough to hold it but you could put some screws in to help it bind. On the two outer sides, rout to fit the shelves (8mm deep). Putting a back on the case will keep it square and give extra strength. Finish the front with some hardwood strips to hide the joins.

If you take the time to set up come cutting and routing jigs to ensure everything is perfectly sized, square and routed in the right spot, it will turn out pretty well.

how do you put screws in when you have the dividers sitting on top of one another?

You shouldn't need to screw every piece. Every 2nd one, going in the opposite direction should be fine. The screws don't add a lot of strength but they help form a tight bond for the glue which provides most of the strength. Plenty of clamps will also help.