I look forward to the day when we can scan an animal brain and see what they think and feel. Till then, I can't comment on whether animals think their babies are 'cute'.

I think 'response-to-cute-stimuli' can be usefully defined on a behavioral level too.

I suggest this definition: the animal is interested in the cute-animal, often despite being strangers; it spends time looking at it or touching it, plays with it or talks to it (depending on the animal's species-typical behavior). But it eventually forgets about it, leaves it behind (or allows it to depart), and does not protect or feed it - as it would an adopted baby. Doing these last things goes beyond "owww it's cute!" and constitutes parenting behavior.

The question is - do animals reliably exhibit non-parenting behavior of the sort described above, and towards what patterns of other animals?