Can dirty injectors cause black smoke on a cummins engine?

yes dirty injectors will cause black smoke.

basically the black smoke is unburnt fuel

dirty injectors usually mean dirty pump as well,but if ya pump is turned up for performance, this will also cause blck smoke

a good dose of injector cleaner thru the system will usually fix, if that's the problem.a little tip, double does it, it will not hurt the system.