Doves and sometimes pigeons make a sound close to that description. Owls make a sound similar, but their call is more of a 'hoo' sound or 'hoot.' If the bird makes a 'cuckoo' sound then it is a cuckoo bird.
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Doves make the very pretty "coo" sound
But if you're looking for the "cuckoo" sound, a la Sound of Music, it is a cuckoo bird :)