Actually, John first did Cocker in Season 1, episode 3, hosted by Rob Reiner. He then repeated it in the next season with Cocker.
IMHO, the first time he did it probably saved the show from being cancelled.
Apparently there was always a fear of being canceled till the later years.
The amazing thing about Belushi’s version of Joe Cocker is that it was probably better than Cocker had done himself for years.
Belushi had been doing it for some time. I saw him do it with National Lampoon's Lemmings tour in the summer of 1974.
There were several actors on that tour that went to be stars with SNL. Chevy Chase did a hilarious parody of John Denver-esque Rocky Mountain songs.