Puttin' on the Ritz (1983) by Taco

At the performance of "Teech and Chong", with Principal Skinner taking over the role of 'Cheech', he is heckled from the audience by Superintendent Chalmers, who tells Skinner that the dessert menu is funnier than he is. The dessert menu is shown, with one of the selections being 'Pudding on the Ritz', a parody of the song 'Puttin' on the Ritz'

Archer is convinced that the pug is barking this song.