Several species of whales - notably the male Humpback Whales (Megaptera novaeangliae) - engage in so-called 'singing' displays. (The songs were first noted by undersea systems installed to detect the movements of submarines.)
“There are numerous hypotheses concerning the nature of humpback song, many of which are not mutually exclusive. The logistical difficulties of studying the behaviour of humpbacks in comparison to songbird's render it challenging, although not impossible.”
The hypotheses mainly centre around breeding, but no direct evidence of the male's songs affecting females has ever been observed.
Theories include : Attracting females, male-male competition, male-male cooperation, vocal arms race, news dissemination etc etc
Audio recordings available via 'The Songs of the Humpback Whale'