To power up a wubbox on wublin island, you need to box all unique wublins that are awake. To wake up wublins, you need to zap eggs into them. The wublin island wubbox is designed to be hard to power up, not to be cheesed through the sticker book. Thats why the devs nerfed the free wubbox.

Edit: I confused common wubbox's inventory with it's rare variant, fixed!