This is what I know of Nubia's involvement in the affairs of Egypt:
c2500 BCE: Nubia in her Kerma phase, lasting about 1025 years.
c1700 BCE: Nubia is known as the Kingdom of Kush (According to the Bible). By this time the Nubians had established sizable cities with a class society of workers, farmers, priests, soldiers, bureaucrats, and an aristocracy with technological and cultural skills on a level with other advanced civilizations of their day. (MT, 10/95, p.10-11)
c1600 BCE: Mounded royal tombs containing artifacts from this time were found in the ruins of the city of Kerma from ancient Nubia. (MT, 10/95, p.10-11)
c1575 BCE: Nubian Kerma sacks Egypt over a period of about 25 years.
1551 BCE: (To 1524 BCE) Amenhotep I (Ahmenophis), son of Amasis I (Ahmose), ruled at the beginning of the 18th Dynasty of Egypt. Inscriptions indicate that he engaged the Nubians in the land of Kush. Some of the southern foes were evidently cave-dwellers (troglodytes), since the inscription goes on to say that 'His majesty captured the Nubian Troglodyte in the midst of his army. (NG, 9/98, p.17)(L.C.-W.P.p.66)(www.ancientroute.com/IndexPharCh.htm)
c1520 BCE: Egypt conquers Nubia, beginning of Egyptian domination of Nubia.
c1500 BCE: (To 1000 BCE) Nubia was colonized by Egypt. (MT, 10/95, p.10-11)
1471 BCE: Tuthmosis III of Egypt built rafts on the Lebanese coast, put them on wagons, and transported them to the Euphrates in order to cross the river and defeat the King of Mitanni. This was his eighth campaign in the thirty-third year of his reign. This was well over 250 miles. He died in the fifty-fourth year of his reign. An inscription at Napata in Nubia tells us about this. (L.C.-W.P.p.87-89)
1345 BCE: Tutankhamen is born.
1323 BCE: Tutankhamen dies.
1069 BCE: (To 945 BCE) This is the period of Egypt’s 21st Dynasty. The capital moved from Tanis to Libyan, to Nubia, to Thebes, to SAIS, and then back to Nubia and Thebes. (www.crystalinks.com/dynasty21.html)
0750 BCE: (To 719 BCE) Piye (Piankhy) ruled Kush (Nubia). In 722 he extended his rule to Egypt. Kashta, ruler of Kush, had begun a campaign against Egypt. With the help of his son, Piankhy, he was successful and Piankhy became pharaoh of Egypt. The Nubian King Piye conquered the weakened and disunited Egypt and became the first of several Nubian Pharaohs who ruled a unified Egyptian and Nubian state for the next century. (eawc, p.7)(MT, 10/95, p.10-11)(www.crystalinks.com/dynasty21.html)
0725 BCE: (To 720 BCE) Tefnakhte I, a prince of western Egypt, ruled as the 1st king of the 24th Dynasty, known as the Sais Dynasty. He attempted to stop an invasion by organizing other Northern Kings with him against invaders from the south. This southern force was comprised of Piankhi’s Nubian forces that wanted to gain control of all of Egypt. The four northern armies under Tefnakht, Osorkon IV of Tanis, Peftjauabastet of Hernopolis, Nimlot, and Input of Leontopolis all enjoyed a relatively easy time in their conquering of the people down to the south, but Piankhi was actually drawing them down. When Tefnakht's forces finally reached Memphis they were massacred and Tefnakht conceded to Piankhi. Tefnakht and the four other leaders were allowed to remain governors of their territories under the new Pharaoh Piankhi. (www.crystalinks.com/dynasty21.html)
0722 BCE: Piye (Piankhy) marched north from Nubia and began his conquest of Egypt where he founded the 25th Dynasty. He consolidated his rule over Egypt and Kush and became the 1st king of the 25th Dynasty. It has been suggested that he revived pyramid building for royals in Egypt, a tradition that had gone extinct for over eight centuries. (www.crystalinks.com/dynasty21.html)(Arch, 9/02, p.55)
0712 BCE: (To 698 BCE) Shebaka of Nubia ruled in Egypt. Some consider him the 1st king of the 25th Dynasty. (www.crystalinks.com/dynasty21.html)
0690 BCE: (To 664 BCE) The Nubian Pharaoh Taharqa, brother of Shebitku, ruled over the upper Nile Nubian-Egyptian state. He is mentioned in the Bible as a pyramid builder. A sculpture of the Kushite king was discovered in the basement of "God's House Tower," an archeological museum, in England in 2000. (MT, 10/95, p.10-11)(SFC, 2/16/00, p.A8)(www.crystalinks.com/dynasty21.html)(Arch, 9/02, p.55)
0593 BCE: The Nubians were defeated by a resurgent Egyptian dynasty after which they moved their capital from Napata to Meroe. (Arch, 9/02, p.56)
0530 BCE: (December) Cyrus the Great, ruler of Persia, died in battle, fighting the Scythians along the Syr Darya. He was succeeded by his son, Cambyses II, who managed to add to the empire by conquering Egypt, Nubia, and Cyrenaica during his short rule. {Persia} (http://en.wikipedia.org/wiki/Cyrus_the_Great)
0270 BCE: The Nubian royals opted for burial at Meroe about this time and pyramids were built there for some 700 years. (Arch, 9/02, p.56)
0180 BCE: The state of Meroe in Nubia was a great cultural center whose scribes developed an alphabet to better express the Nubian language around this time. (MT, 10/95, p.10-11)
So, for a period of at least 1400 years, Nubia and Egypt had extensive dealings with each other, so King Tut may have been of Nubian descent.