If you decrease the number of loop cuts and give the bendybone more segments it looks better. I gave the bendybone 30 segments. You can also give it a subdivision level of 3. Experiment a bit with the loopcuts and segments to find the right balance.
You can always delete loopcuts (press x and select ‘Edge Loop’ with a loopcut selected) and play with the number of segments wile parented. But if you add loopcuts you will have to re-parent again.

If you wish more control for animating your cube I have to redirect you to our rigging expert DanPro.
Blender Rigging Advanced Tentacle Rig Part 1
There is also a rigging tutorial by Kent Trammel who tackles this in a different way.
Rigging a Spiral Phone Chord in Blender