Who are those who claimed to be gods and are mentioned in the Quran?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

The Quran tells us about two persons who claimed divinity. The first one was Namrood ibn Kan‘aan (Nimrod), the king of Babylon. Allaah The Almighty Says (what means) about him: {Have you not considered the one who argued with Abraham about his Lord [merely] because Allaah had given him kingship? When Abraham said, “My Lord is the one who gives life and causes death,” he said, “I give life and cause death.” Abraham said, “Indeed, Allaah brings up the sun from the east, so bring it up from the west.” So the disbeliever was overwhelmed [by astonishment], and Allaah does not guide the wrongdoing people.}[Quran 2:258] Ibn Katheer mentioned that he argued with Ibraaheem (Abraham) about the existence of his Lord and claimed that he was God and that there was no other god except him.

The second one was Fir‘awn (Pharaoh), may Allaah curse him. Allaah The Almighty Says about him (what means): {And Fir‘awn said, "O eminent ones, I have not known you to have a god other than me.}[Quran 28: 38] He said to Moosa (Moses) (what means): {[Pharaoh] said, "If you take a god other than me, I will surely place you among those imprisoned.”}[Quran 26:29]

And Allaah Knows best.