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

I doubt you will hear a difference. But if you will feel better, and want bragging rights, buy a couple 8 ga PC’s. 
 

so, you have 8ga from your box :) to outlets,?…..I would probably grab a medium cost 8ga cords, more money does not mean 10x better. 
 

use your best judgement. 
 

years ago, I bought 30feet of 8ga speaker cable, I have to cut them to fit in the banana plugs. 
 

NO! Because even a 14 gauge power cord is rated to handle 15 amps/ 1500 watts. This is the same rating for the typical breaker box/AC outlet found in most homes. That's a lot of power! Increasing the size/diameter of a power cord is only required if you plan to use an arc welder! Then you need a lower gauge/thicker cord. For a 200wpc amp a 14 gauge cord is perfectly fine. You don't need a garden-hose size power cord!

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.