Puzzle #136: Square Hearts?

Hearts is a card game for three or four players. Each turn, either 26 points are distributed amongst two or more of the players, or every player gets 26 points except one player who gets none. A game is over when one or more players reach 100 or more points. The low score wins.

Is it possible in a three-player game for each players’ score each turn to be a square? How about in a four-player game?

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, January 13, 2016 at noon Pacific Time. I will post the answer shortly after.