Jamieson, Fausset and Brown on Isaiah 43:3

3. Egypt for thy ransom--Either Egypt or Israel must perish; God chose that Egypt, though so much more mighty, should be destroyed, in order that His people might be delivered; thus Egypt stood, instead of Israel, as a kind of "ransom." The Hebrew, kopher, means properly "that with which anything is overlaid," as the pitch with which the ark was overlaid; hence that which covers over sins, an atonement. Nebuchadnezzar had subdued Egypt, Ethiopia (Hebrew, Cush), and Saba (descended from Cush, Ge 10:7, probably Meroe of Ethiopia, a great island formed by the Astaboras and the Nile, conquered by Cambyses, successor of Cyrus). Cyrus received these from God with the rest of the Babylonian dominions, in consideration of his being about to deliver Israel. However, the reference may be to the three years' war in which Sargon overcame these countries, and so had his attention diverted from Israel (see on Is 20:1) [Vitringa]. But the reference is probably more general, namely, to all the instances in which Jehovah sacrificed mighty heathen nations, when the safety of Israel required it.