Which powerful Asian army drove the Kushites out of Egypt?

The powerful Asian army that drove the Kushites out of Egypt was the Assyrian army. The Assyrians, with their advanced military technology, including iron weapons and cavalry, were able to defeat the Kushites and end their control over Egypt during the late 8th century BCE.

The event you're asking about is a part of ancient Near Eastern history. The Assyrian Empire was a force to be reckoned with during its zenith, particularly between the 9th and 7th centuries BCE. They were known for their military prowess, strict discipline, and innovative tactics, which included the use of siege engines and iron weaponry—technology that was superior to the bronze weapons used by many of their adversaries.

The Kushite period in Egypt is also referred to as the 25th Dynasty, during which the Nubian kings ruled Egypt, having been based in what is now modern Sudan. The Kushites embraced much of the ancient Egyptian culture, religion, and kingship. However, the Assyrian incursions into Egypt marked the end of Kushite power in the area. The decisive military campaigns by the Assyrian king Esarhaddon, and later his son Ashurbanipal, eventually compelled the Kushite king Taharqa and his successor, Tanutamun, to retreat to Nubia, thus ending their reign over Egypt and bringing Egypt back under the influence of the Assyrian Empire for a brief period before the rise of the succeeding Neo-Babylonian Empire.