I thought that one was a Randy Newman joint.

I have nothing against Cocker, but his death is no really a big loss to the popular music. Only good song I know from him is that version of that Beatles tune. And really haven´t got even that.

Without the added "e", yes it was.
I think Cocker's most famous performances are covers (that from 9 1/2 weeks, and his rendition of "With a little help from my friends" from Woodstock, probably?). But honestly I'm not at all familiar with his output/other potential hits he recorded. As Genteel said, when someone talks about Joe Cocker the only song in my head is that Randy Newman cover. But my perception of his actual fame could easily be a bit distorted (being in Berluscoland etc. etc. ).

these are some of the images that came up when googling "RIP Joe Cocker"