Xerxes I’s father was Darius I, whose earlier invasion ended at the Battle of Marathon.
Darius I ruled the Achaemenid Persian Empire from 522 to 486 BC. His expedition against Greece in 490 BC followed Athenian and Eretrian involvement in the Ionian Revolt, including the burning of Sardis. Persian commanders Datis and Artaphernes led the campaign, which culminated in the defeat at Marathon.
Darius planned a larger invasion after Marathon, but revolts in Egypt delayed him. He died in 486 BC while preparing for further campaigns, and his son Xerxes succeeded him. Xerxes then organized the second Persian invasion of Greece, which began in 480 BC and included Thermopylae, Artemisium, and Salamis.
The names can be confusing because several Achaemenid rulers shared similar royal titles. Cambyses II was Darius’s predecessor, while Artaxerxes I was Xerxes’s son and successor. Cyrus I is also not the standard name of the ruler meant in this question; Cyrus the Great founded the empire’s imperial dynasty.