Cut a strip of fabric 26 mm longer than the circumference of the box and 26 mm wider than the height of the box. Cut a circular piece of fabric 3 mm smaller in diameter than the bottom of the box.
Thin white glue with water just enough to make it easy to apply. Brush it onto the exterior of box. Wrap the fabric around the side of the box, centering the box in the middle of the strip, smoothing it as you go. Overlap the ends of the fabric.
Apply glue onto the inside of the box along the edge. Fold the excess fabric over the top edge of the box to the inside. Cut small slits along the fabric if necessary for a smooth fit.
Apply glue to the bottom of the box and glue the fabric to the bottom. Cut small slits in the excess fabric that will be folded over the bottom of the box, to make sure the box will sit flat.
Glue the circular fabric to the bottom of the box.
Cut a circular piece of batting the size of the lid and glue it to the top. Cut a circular piece of fabric large enough to go over the batting and the side of the lid.
Cut small slits in the part of the fabric that will extend over the side and glue the fabric to the side of the lid.
Cut a piece of fabric three times the width of the side of the lid and the length of the circumference plus a small overlap. Fold the fabric in thirds width-wise and glue it around the side of the lid.
If desired, lay the inside of the box with a large circular piece of fabric and glue it only around the edge so that the fabric will hang loosely inside the box rather than conform to the box's shape.