Hallo Headphonecrazy,
All cables that leave my house are checked and should work properly. Of course a cable may break, but by experience most problems that appear with the HD600 are due to the rather lousy connection inside the earcups of the phone. The two small pins of the cable make just contact to a very small and vulnerable spring. Contact area is truly minimal.
Also, be aware that the connectors should be put in the first time with some force. When many problems arose with the first series of HD600s Sennheiser changed the opening in the marble-like "strap" through which the connector passes. There now is a very tight fit that should prevent small movements of the connector. If the connector isn't brought in deep enough contact will not be made.
Tip, exchange the left and right connectors of the cable. If the problem also changes channels, than the cable indeed is defective. Of course defective cables will be immediately replaced.
Do you have a multimeter and are you able to measure resistances?
Cheers,
Jan