Jamieson, Fausset and Brown on Jeremiah 25:26

26. Sheshach--Babylon; as the parallelism in Jr 51:41 proves. In the Cabalistic system (called Athbash, the first Hebrew letter in the alphabet being expressed by the last) Sheshach would exactly answer to Babel. Jeremiah may have used this system (as perhaps in Jr 51:41) for concealment at the time of this prediction, in the fourth year of Jehoiakim, while Nebuchadnezzar was before Jerusalem. In Jr 51:41 there can be no concealment, as Babylon is expressly mentioned. Michaelis more simply explains the term "brazen-gated" (compare Is 45:2); others, "the house of a prince." Rather, it comes from the Babylonian goddess, Shach, by reduplication of the first letter; from her Misael was named Meshach by the Babylonians. The term Shace was applied to a festival at Babylon, alluded to in Jr 51:39, 57; Is 21:5. It was during this feast that Cyrus took Babylon [Herodotus, 1]. Thus Jeremiah mystically denotes the time of its capture by this term [Glassius].