The earliest marathon showing of episodes of a show that I remember watching a lot of was the Dick van Dyke Show on Nick at Night. It looks like it was in 1991. I think that they showed about 20 episodes per night for a week or so.

Were there earlier marathons than this, where a whole series was shown?

MTV didn't show all of The Monkees episodes but did show 46 of 58 over 22 1/2 hours.

Nick at Nite promoted the Donna-thon in 1990 as the first ever week-long marathon of a TV show, but it obviously wasn't the entire Donna Reed Show series because they didn't have the rights to the whole series.