Was Cush the father of Nimrod?
There does seem to be some question if Cush is Nimrod's father. Note some of the Biblical commentaries:
Ellicott's Commentary for English Readers
(8) Cush begat Nimrod.—This does not mean that Nimrod was the son of Cush, but only that Cush was his ancestor. In the days of Nimrod population had become numerous, and whereas each tribe and family had hitherto lived in independence, subject only to the authority of the natural head, he was able, by his personal vigour, to reduce several tribes to obedience, to prevail upon them to build and inhabit cities, and to consolidate them into one body politic.
Barnes' Notes on the Bible
In this episode Genesis 10:8-12, the author turns aside from the table of nations to notice the origin of the first great empires that were established on the earth. "And Kush begat Nimrod." The author had before enumerated the sons of Kush, who were heads of nations. Here he singles out one of his sons or descendants, who became the first potentate of whom we have any record. He notices his qualities for rising to this position among men. "He began to be a mighty one in the land. He was mighty in hunting, before the Lord." Hunting is a comprehensive term, indicating the taking of any species of animal, whether of the air, the sea, or the land. Nimrod's distinction in this respect was so great as to become proverbial.
Gill's Exposition of the Entire Bible
And Cush begat Nimrod,.... Besides the other five sons before mentioned; and probably this was his youngest son, being mentioned last; or however he is reserved to this place, because more was to be spoken of him than of any of the rest. Sir Walter Raleigh (i) thinks that Nimrod was begotten by Cush after his other children were become fathers, and of a later time than some of his grandchildren and nephews: and indeed the sons of Raamah, the fourth son of Cush, are taken notice of before him: however, the Arabic writers (k) must be wrong, who make him to be the son of Canaan, whereas it is so clear and express from hence that he was the son of Cush.
Verse 8. - And Cush begat - not necessarily as immediate progenitor, any ancestor being in Hebrew styled a father - Nimrod; the rebel, from maradh, to rebel; the name of a person, not of a people; - Namuret in ancient Egyptian. Though not one of the great ethnic heads, he is introduced into the register of nations as the founder of imperialism. Under him society passed from the patriarchal condition, in which each separate clan or tribe owns the sway of its natural head, into that (more abject or more civilized according as it is viewed) in which many different clans or tribes recognize the sway of one who is not their natural head, but has acquired his ascendancy and dominion by conquest.
So Nimrod was a descendant of Cush, but whether he was the son, grandson, or great-grandson is not detailed in the scriptures. Commentators do seem to lean to Cush not being the direct father of Nimrod.
It should also be noted that the term "father" can be used for descendants other than direct sons or daughters. For additional information on this, see the topic "Father" in the Insight on the Scriptures.