Trying to upgrade items in the cube is just like gambling. If you're lucky, you'll get what you're looking for quickly. If not, it can take many, many, many tries. Better just to do rifts/ greater rifts and find a good legendary item.
The item for socketing only works on weapons. It's called Ramalandi's Gift, and can drop anywhere, but only in Torment 1 or higher games.
Ambition is a poor excuse for not having enough sense to be lazy.