With the god Apollo, Hecuba had a son named Troilius. An oracle prophesied that Troy would not be defeated as long as Troilius reached the age of twenty alive. He and his sister, Polyxena, were ambushed and killed by Achilles during the Trojan War.
Polydorus, Priam's youngest son, was sent with gifts of jewelry and gold to the court of King Polymestor to keep him safe during the Trojan War. The fighting was getting vicious and Priam was frightened for the child's safety. After Troy fell, Polymestor threw Polydorus to his death to take the treasure for himself. Hecuba, though she was enslaved by the Achaeans when the city fell, eventually avenged her son.
Apollo also fell in love with Cassandra, daughter of Hecuba and Priam, and Troilius's half-sister. He promised Cassandra the gift of prophecy to seduce her, but she rejected him afterwards. Enraged, Apollo--unable to take back his gift--cursed her, so that no one would ever believe her prophecies.