Egypt and Ethiopia

Previously in Herodotus

110. He moreover alone of all the Egyptian kings had rule over Ethiopia; and he left as memorials of himself in front of the temple of Hephaistos two stone statues of thirty cubits each, representing himself and his wife, and others of twenty cubits each representing his four sons: and long afterwards the priest of Hephaistos refused to permit Darius the Persian to set up a statue of himself in front of them, saying that deeds had not been done by him equal to those which were done by Sesostris the Egyptian; for Sesostris had subdued other nations besides, not fewer than he, and also the Scythians; but Darius had not been able to conquer the Scythians: wherefore it was not just that he should set up a statue in front of those which Sesostris had dedicated, if he did not surpass him in his deeds. Which speech, they say, Darius took in good part.

- Herodotus, Book II

More Information: Egypt, Herodotus's Book.

I think H is talking about Nubia (modern Sudan). There is no recorded Egyptian conquest of Ethiopia.