John Gill Commentary Deuteronomy 31:29

"For I know that after my death ye will utterly corrupt yourselves, and turn aside from the way which I have commanded you; and evil will befall you in the latter days; because ye will do that which is evil in the sight of Jehovah, to provoke him to anger through the work of your hands." — Deuteronomy 31:29 (ASV)

For I know that after my death
Which was just at hand, some time after that, not immediately; this he knew by a spirit of prophecy, namely, what follows:

you will utterly corrupt [yourselves] ;
your ways, works, and manners, and so yourselves; corrupt the worship of God by making idols, and serving them, which is the corruption chiefly intended:

and turn aside from the way which I have commanded you :
from the way of the commandments of God, which Moses had given them in his name, and in which they were directed to walk; but, as here foretold, would wander and swerve from them as they did:

and evil will befall you in the latter days ;
not only in the times of the judges, and in the time of the Babylonish captivity, but in their present captivity, as they call it; which shows that the following song has things in it which respect times at a great distance, and even the present ones, and yet to come:

because you will do evil in the sight of the Lord, to provoke him to
anger through the work of your hands ;
their idols, idolatry being the evil chiefly designed, which is of all things the most provoking of the Lord.