Ill try and explain a native English speakers perception of the aforementioned.
I could have done it //I could have done it, but i chose not to. (Had no intention to do it at the time of occurrence.)
I would have been able to do it //I would have been able to do it, but someone stopped me. (Had desire to do it at occurrence but was prevented by something else.)
I could have been able to do it ? // This is technically incorrect, "could" and "able" are incompatible like this. Perhaps it might make sense if it were referring to a previous event before an occurrence of it. "I could have been able to do it, but i didn't take the time to study before the test." Even then it doesn't really sound right.
Hope this helps! :) Welcome by the way.