וַיִּכְתֹּ֥ב מֹשֶׁ֛ה אֶת־הַשִּׁירָ֥ה הַזֹּ֖את בַּיּ֣וֹם הַה֑וּא וַֽיְלַמְּדָ֖הּ אֶת־בְּנֵ֥י יִשְׂרָאֵֽל׃
So Moses wrote this song the same day, and taught it the children of Israel.
Find Talmudic references to Deuteronomy 31:22: , passages from the Talmud Bavli and Yerushalmi.