Cut four 12-by-12-inch pieces of 1/2-inch plywood with a saw. Cut a 12-by-11-inch piece as well.
Assemble the 12-by-12-inch pieces into a four-sided box.
Glue the box together with wood glue and clamp it together with bar clamps.
Wipe off any wood glue that oozes out from the joints with a paper towel.
Nail each corner together with five 4d finishing nails spaced every 2 inches.
Allow the glue to dry for the time recommended on the bottle.
Glue the 12-by-11-inch piece into one end of the box and use more nails to secure it in place. It will form the back. Allow the glue to dry.
Drill three 1/8-inch holes through the center of the box's back positioned in a line vertically.
Paint the wall cube as desired.
Use a stud finder to locate the positions of studs within your wall.
Place the cube on the wall with the holes lined up with the studs.
Drill a 1/16-inch pilot hole through each of the three holes in the cube and into the stud behind it.
Screw the cube to the wall with three 3-inch wood screws. Paint the screw heads to match the cube if desired.