A:
You can, but in order to connect all 3 of your devices, you may need to connect one of your devices to the Component port. While component is analog, it still provides a full High Definition signal.
So if you connect your Cable Box (since that would be the most likely device with component Red-Blue-Green & Audio Red/White outputs) to component, and the Apple TV to your HDMI input, you should be able to connect all three devices to your television.
If we can help further, please reach out and let us know how we can help.
--Mr. Samsung