Cuddlefish is a fictional American rock band based on the band Reel Big Fish. They were first mentioned in iPilot after Carly had to cancel going to a Cuddlefish concert (on a Saturday) because Ms. Briggs made her judge the talent show auditions instead.
Sam traded a T-shirt Carly made for her (to celebrate their five year anniversary of being friends) to Rip-off Rodney in exchange for two tickets to a sold-out Cuddlefish concert, so she and Carly could attend it together in the episode iDon't Want to Fight. In that episode, Freddie mentions Carly really likes Cuddlefish, it being her favorite band.
Cuddlefish was mentioned in iLike Jake as well. When Jake comes over to Carly's apartment, and they go upstairs to the webshow area, Carly plays a song through the speakers by accident. Jake then comments that the song is titled "Brake Lights" by Cuddlefish.