Do I need 10 gauge power cord if I have 10 gauge from panel?

I would not worry so much about the gauge as the intent of the cord and the quality (it is likely to be 10 gauge) These days most cable companies build a special cord for amps as opposed to low power components.

I searched for nearly a year to get the power cord right on my amp. Finally I found the Audio Quest Hurricane. Wow, this is a really good power cord… the dealer who brought it over told me his employees asked for it because of all the buzz on line… the buzz. There is good reason for all the buzz. It is very neutral and quiet.

I guess the short answer is, yes definitely you want to find a better cord. 

it is unlikely a 14 gauge power cord is not negatively impacting the sound.

No.

I am unaware of any amp requiring a 10 gauge power cord. What amp/amps do you have? Why did you install 10 gauge wire to the breaker box/AC outlet? None of your gear combined will draw that much current. Stoves, refrigerators and washing machines/dryers run on 240 volts/30 amp circuits. 

@ghdprentice :"It is unlikely a 14 gauge power cord is not negatively impacting the sound." That is poor grammar! Do not use a double negative in one sentence. The correct sentence is: It is likely a 14 gauge power cord is negatively impacting the sound.