Welcome to the forum! Yes, replace both the brake cable and its housing. I'm assuming this will be a good first project for you in bike repair. Do you know if you have a "Bike Coop" in your area? Check around whatever college campus is closest to you, almost guaranteed to be one.

If so, just take your bike down there and the volunteers working there will walk you through the repair free of charge. Bike Coops are a great thing to participate in for hands on guidance. You can give back by helping out others as you become more experienced too.

YouTube tutorials are also very good for visual guidance. Buy Park Tool Repair Manual for written instructions, and of course you have the best community for web interactions right here, and remember, the search button and archives here are your friend.