Add padding to contact section?

I'm trying to add some padding to my "Contact Me" section. 

But for some reason the border won't "pad" alongside the contents. So the border remains where it is while adding padding moves the buttons/etc downwards. It looks quite odd.

Go here -> https://nein-mc.neocities.org/csstest/

Then put in this:

Then you should see what I mean.

How do I fix this?