SX2210 Sound Options??

I have a motorola cable box (DCH-3200) connected to my SX2210 monitor via hdmi. I also have my computer connected (DVI) to my SX2210. I can toggle between "seeing" the computer on the monitor or "tv" via input select menu.

I also want sound. Could I go from the audio out on the cable box to the audio in on the monitor and then go audio out on the monitor to a sound bar?

Anyone tried this? If this is a question for another forum, please suggest.