If we place cuckoo birds in captivity, with plenty of artificial nests and environment which is close enough to their natural habitat, are they going to reproduce and demonstrate maternal care of their own offspring, because they don't have any other choice?

Good question to which I think the answer is... we don't know.

Cuckoos are considered obligate brood parasites which means that - as far as we can tell - they always leave offspring care to the species they parasitise under relevant ecological conditions. In the scenario you suggest my best guess is they would not reproduce, but without doing the expt we won't know for sure.

My thoughts exactly. If there are no nests of other species I don't see how they reproduce. AFAIK they have no ability to incubate their own eggs.