Every single episode. That is somewhat of a stupid question. He is in the glee club. He must sing. lolz. :)
The Glee Episode In Which Finn Happens To Sing Jesse's Girl To Rachel Is Laryngitis
Season 2 episode 8, Furt
It was featured in Pilot and Hairography, both by Finn and Rachel.
In the episode "Showmance" of Glee, Finn sings "I'm Gonna Be (500 Miles)" by The Proclaimers in the shower.
There is an episode on Glee called 'The Quarterback' which is a tribute episode towards Finn Hudson (Cory Montieth)
Lea Michele (Rachel) and Cory Monteith (Finn) sing a duet of No Air on Glee!
season 3 episode 10
Episode 5 ' The Rhodes Not Taken'
Finn proposes to Rachel at the end of "Michael."
Finn dresses in a red Gaga costume (made from a shower curtain) in the "Born This Way" episode which is the 18th episode of Season 2 and the 40th episode of Glee overall.
im not sure but you can find it in the list of episodes of glee in wikipedia
Season 1, episode 20 - Theatricality. :)