It is really important that you remember one rule when factoring: always factor out the greatest common factor first, before factoring with grouping, etc. If you didn't make a typo, yes, add like terms first. If this is the correct problem, I would assume that your teacher is making sure you know to factor out the GCF first and that is all. That IS a form of factoring in itself. So,
3g^{3} - 51g + 210g
3g^{3 }+ 159g
3g(g^{2} + 53)
By the way, as an algebra teacher of more years than I care to share : ) I have been known to give a problem like this. It does show complete understanding.
Ms. B.