Therefore will I cast you out of this land into a land that ye know not, neither ye nor your fathers; and there shall ye serve other gods day and night; where I will not shew you favour.
Serve other gods - that which was their sin in their own land was their punishment in exile. Retribution in kind. They voluntarily forsook God for idols at home; they were not allowed to serve God, if they wished it, in captivity (Daniel 3:1-30; Daniel 6:1-28 illustrate this strikingly).
Day and night - irony. You may there serve idols, which ye are so mad after, even to satiety, and without intermission.