"Yamaha HTR-6030 Receiver, a Motorola DCT6416 DVR/Cable Box, and a Samsung UN55ES7100 TV"
"I ran a optical cable from the input on the receiver to the optical output on the DVR but I am not getting any sounds"
- From your description - you only have a cable box, a receiver and a TV. I know this sounds obvious - but do you have speakers connected to the receiver? If No - that is your problem, as a receiver will process the signal and output them to speakers that will make the sound.
If you do have speakers connected and just did not mention it - then you can start debugging. Start with the source and work your way through it. Does the cable box have a setting that lets it know to send a signal through the cable you are trying to use?
Do you need to turn the optical out signal (or whatever your cable box calls it) on at the receiver first?
If that is set - then you need to make sure that your receiver is set to receive the input from that cable. What is the optical input on the receiver you hooked it up to called? Whatever that connection is called, you need to set the receiver to that. If you set the receiver to TV - but the signal is coming in on optical 1 input - you will never hear it.