For large copper cables, I use nitric acid
Rinse well afterwards.
Be careful, use gloves and protective glasses, this acid is highly corrosive.
Yikes, a little too well I would think!
HCl also dissolves copper oxides nicely, but the problem with acids (especially mineral acids) is, they stick in pores in the metal, and never really rinse away. So you can wash with HCl, then rinse several times with neutral water and mild base, and get a clean surface ... that some months later, still inevitably turns green (not just deeper copper, then brown).
It's a good combination when the pores are about to be permanently covered, like for tinning, galvanizing, electroplating, etc. For this reason, try to cover the entire surface, even if you don't need to.
I've also had material that's so porous on the surface (after the acid) and doesn't tin well. If it's covered in rust or scale, you're probably best off with a mechanical solution for this reason.
Tim