Note that these are all cockatiels, very intelligent parrots that will readily pick up and replay sounds they hear. This is quite distinct from sparrows and most songbirds, which only seem to pick up certain songs.
Even more fascinating, in my opinion, are Lyrebirds [0]. They have been observed the imitate artificial (human-made) sounds such as those of camera shutter, chainsaws [1], and construction work [2].
Not only do I find it impressive that they're capable of producing these kinds of sounds, but probably much more the necessary memory-recall for this. Birds have rather little brain-mass after all, so they must have some excellent way of 'sampling', distinguishing, and storing auditory stimuli.
I expect that, sometime before I die, there will be a clip of a lyrebird doing a David Attenborough narration of a clip of a lyrebird imitating David Attenborough marvelling at some sound that a lyrebird is making.
