Parece que seu /etc/apt/sources.list
está absolutamente quebrado.
Tente preenchê-lo com o seguinte conteúdo:
deb http://archive.ubuntu.com/ubuntu xenial main restricted universe
deb http://archive.ubuntu.com/ubuntu xenial-updates main restricted universe
deb http://archive.ubuntu.com/ubuntu xenial multiverse
deb http://archive.ubuntu.com/ubuntu xenial-updates multiverse
deb http://archive.ubuntu.com/ubuntu xenial-security main restricted universe
deb http://archive.ubuntu.com/ubuntu xenial-security multiverse
deb http://archive.canonical.com/ubuntu xenial partner
Em seguida, execute:
sudo apt-get update
sudo apt-get dist-upgrade
sudo apt-get install mysql-server