I once made two sets of braided cables, one copper, the other silver.
The similarities because of the braided design compared to co-ax was quite clear, braided sounded more open.
The differences were smaller but still clearly noticable:
the copper one sounded more pleasant, to my ears because the treble was less smooth but also very slightly rolled of, and the bass was warmer, to my ears due to less definition.
The silver cables missed bass warmth but the bass was better defined and seemd to go deeper, the treble was equally more extended and detailed.
But despite these criticisms, the copper one actually sounded more pleasant, less analytical, more midranged-biased, perhaps covered up inperfections elsewhere in the system.
So yes, it seems copper seems to add a slight euphonic distortion, warmth if you like.
But keep in mind the usual caveats; cables are systemdependent, the wire was not exactly the same and other configurations can give other results, there are different kinds of copper etc.
Differences between cables might be characterized as small, but the difference between pleasant and unpleasant, or between ugly and beautiful can be small too, seen quantitativaly.
For what it's worth: Ray Kimber once in an interview in Hifi News a decade ago explained the dfifferences because of the material differences; he compared copper to a candybar, brittle and slightly irregular, and silver with a wax candle, very homogenous.