I made a fabric-covered box for Mother's Day. I used to make a lot of these in the late '90s, but the company no longer makes the kits with the cardboard already perforated and scored for easy punching out and bending.
You can still get some kits and patterns from them. Please check them out! Calico Moon - Boxabilities. This was the last kit I had. I will miss them.
Pattern and instructions were great: Trace and cut the fabric from the pattern pieces. Use Heat N Bond to fuse the fabric to the cardboard. Use Aleene's Tacky Glue to seal the deal.
I've made other fabric-covered boxes, but these were a real treat. Excellent designs. If you have any other sources for fabric-covered boxes and bins, please let me know.