Arrange two 16-by-16-inch boards to rest upright across from one another with 14 inches between them. Set the two 14-inch boards upright between the two 16-inch square boards to form a cube. Drill three evenly spaced 3-inch wood screws into each corner to hold the cube together.
Place one of the two remaining square boards over the cube to be the bottom and align the edges to make the piece flush on all sides. Drill three evenly spaced 3-inch screws through the bottom board and into the cube frame on all four sides to secure.
Sand over the cube unit inside and out to smooth the wood. Apply a wood stain or paint, as preferred, over the outside of the cube to suite the décor of your room. Allow the material to dry for two to three hours.
Apply a clear sealant over the stain or a second coat of paint, if desired, and allow to dry. Turn the cube upside down with the opening facing down. Stick a felt pad to the bottom board at each corner to protect your floors. Flip the cube over to rest with the opening facing up.
Spread your fabric onto a flat surface with the pattern facing down. Center your square of foam over the fabric. Place the remaining 16-inch square board centered over the foam.
Lean on the board and wrap the fabric around to the back. Secure the fabric to the back of the board with a staple gun, inserting a staple every 2 inches around all four sides.
Lay your plywood over the back of the board to cover the fabric edges. Center the plywood so 2 inches of board overhang the plywood on all four sides. Secure the plywood to the board with 2-inch wood screws at each corner of the plywood and in the center of the board. Flip this cushioned unit over and set over the opening of the cube.