The Kingdom of Kush was an ancient state that existed (twice) in what is now the northern part of The Sudan.
The first Kingdom of Kush developed around the settlement of Kerma (just above the third cataract on the Nile, in Upper Nubia). Although the Kingdom of Kush existed during the ancient Egyptian Old and Middle Kingdoms (2686 to 1650 BCE), Kerma reached its zenith during Egypt's Second Intermediate Period (1650 to 1500 BCE). The Ancient Egyptians referred to its inhabitants as the 'people of Yam'.
At the end of the Middle Kingdom (1650 BCE), Lower Egypt fell under the control of the Hyksos, and Upper Egypt (particularly Nubia) was in disarray. During the Second Intermediate Period Upper Egypt was dominated by the Kush. But the resurgence of a united Egypt with the 18th Dynasty (1550 to 1295 BCE) brought the first kingdom of Kush to an end. New Kingdom Egypt (1550 to 1069 BCE) established control as far south as the fourth cataract and created the post of Viceroy of Kush, governing Nubia as a separate region (in two parts: Wawat and Kush).
Egyptian control over Nubia declined, and by the eleventh century BCE, the Viceroys of Kush had become independent kings. During the Egyptian Third Intermediate Period a new Kushite kingdom emerged. By the late Period (747 to 332 BCE) Egypt had fallen under the control of Kush, and by the time of Piye the whole of Egypt, right up to the shores of the Mediterranean, was under Kush administration. But it was not to last -- in 671 BCE Egypt was invaded by the Assyrians, and by 654 BCE they had driven back the Kush back into Nubia.
Kush remained safe behind the desolate landscape south of Aswan, developing a separate language and variant architecture. (It did, however, maintain the pharaonic tradition.) Eventually the capital was moved from Napata south to Meroe where a new 'Merotic' kingdom developed.