No, cubing gives you back 1~3 dura.
Ryuch pretty much said most of it. The only problem would be your shoes.
Since only normal Movement Puzzles exist, that's 10~15 dura off per enchant. If you're lucky enough, you might get enough dura left to upgrade up to +8. Since it's one of the gears that use normal puzzles, I would aim for at least 230+ dura just to be safe on enchant and upgrade.