with a long needle, and some strong thread, you can make that 'cube' more cube-shaped.
just use the thread to pull facing sides together on all 3 axis. several places on each axis to make it less noticable... id say 4 places all around the circle surrounding the heart. Make a small stich (pink thread if possible) then push the needle and thread through to the other side of the cube, also on the circle, pull the desired amount of tension, and make another stitch. One should note that unless you use strong thread, the threads can break if you distort the cube, or if you dont do many threads per side, that they could rip the cube when distorted...
alternatively would be to unstitch a seam, unstuff the cube, and actually sew in "cells" to make the center rigid enough to hold more of a cube shape... this is more difficult but should prove more stable.
If I get one I'll mess around with it...