Who was the Cyclops' father?

Answer 1

Well there was a smithy race of Cyclopes whose parent were Gaea (Mother Earth) and Uranus (Father Sky), they were bound in the Underworld by their father for their ugliness, but in later myth Poseidon was the father of the Cyclops, Polyphemus, who Odysseus killed.
There is more than one cyclops, and they have different fathers. The original three Cyclopes were sons of Ouranos (Uranus) and Gaea. He was so appalled by his offspring, and fearful of their great size, that he imprisoned them in Tartarus.

The other well known Cyclops was Polyphemus, the cyclops shepherd that trapped Odysseus and his crew, devouring them. That Cyclops was an offspring of Poseidon.