Thank you for the compliment, this library/reading niche turned out really well and the clients love spending time there!

To answer your question:

The inside clear space of each cubby space is: 13” wide x 13” tall x 11-1/2” deep

Wonderful. And the back is just painted wall?

It's painted wood, it's part of the cabinet. You need a back panel for structural support.

That was quick. Thanks!!!!!! Beautiful!