Measure two 12-by-12-inch and two 12-by-11-inch pieces of plywood. Measure one 12-by-12-inch piece of luan, a type of light plywood. Cut each piece with a saw.
Overlap the ends of the 12-by-12 pieces with the 12 inch sides of the 11-by-12 pieces and glue with wood glue. Use clamps to hold it together while the glue dries. Once dry, use 4 nails to secure each edge on the top and bottom of the cube. Hammer each nail so it sits a few millimeters below the surface of the wood.
Glue the 12-by-12-inch piece of luan to the back of the box. Use four nails on each side to secure it. Hammer each nail so it sits a few millimeters below the surface of the wood.
Putty each nail hole with wood putty and let it dry. Sand the entire box.
Paint the cubby and let it dry. Sand and add a second coat of paint if desired.
Mount the cubby on the wall by holding it in place and drilling through each of the four corners of the back panel and into the wall. Use 2-inch screws fitted with washers to secure the cubby.