I have a cuckoo clock, and its notes are Db - A.

I listened to a cuckoo on YouTube, and its notes don't seem to be strictly on the scale. I believe its notes are D and then a note partway between B and Bb.

The European cuckoo says "cuckoo." It lays its eggs in other birds' nests. Hence the many tunes satirically called "The Cuckoo's Nest."

The American cuckoo (yellow-billed cuckoo) says something like "Glerk." It's a more upstanding citizen and raises its own young. Does anybody write a song praising it for its respectability? Of course not.