Não consigo instalar o MySQL

Bom dia!

Ao executar o comando de instalação do MySQL, é apresentado o erro abaixo:

***********
sudo apt-get install mysql-server
Reading package lists...
Building dependency tree...
Reading state information...
E: Unable to locate package mysql-server
***********

Att.

Óbvio, o pacote mysql-server não existe nos repositórios.

Já verificou rodando apt-cache search mysql para verificar quais pacotes são encontrados? Você pode ver isso graficamente também, através do Synaptic.

Outra coisa que pode estar acontecendo, é que seu sistema não está atualizado.

Desculpe, para mim não é tão Obvio...

Quando executei o comando "sudo apt-cache search mysql" retornou o erro "rsyslog - reliable system and kernel logging daemon"

Além disso executei o comando de update e deu outro erro, conforme log abaixo:

Ign:1 http://security.ubuntu.com/ubuntu xenial-security InRelease
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400 Bad Request [IP: 91.189.88.149 80]
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Ign:44 http://br.archive.ubuntu.com/ubuntu xenial-updates/main Translation-en
Ign:45 http://br.archive.ubuntu.com/ubuntu xenial-updates/restricted amd64 Packages
Ign:46 http://br.archive.ubuntu.com/ubuntu xenial-updates/restricted i386 Packages
Ign:47 http://br.archive.ubuntu.com/ubuntu xenial-updates/restricted all Packages
Ign:48 http://br.archive.ubuntu.com/ubuntu xenial-updates/restricted Translation-en
Ign:49 http://br.archive.ubuntu.com/ubuntu xenial-updates/universe amd64 Packages
Ign:50 http://br.archive.ubuntu.com/ubuntu xenial-updates/universe i386 Packages
Ign:51 http://br.archive.ubuntu.com/ubuntu xenial-updates/universe all Packages
Ign:52 http://br.archive.ubuntu.com/ubuntu xenial-updates/universe Translation-en
Ign:53 http://br.archive.ubuntu.com/ubuntu xenial-updates/multiverse amd64 Packages
Ign:54 http://br.archive.ubuntu.com/ubuntu xenial-updates/multiverse i386 Packages
Ign:55 http://br.archive.ubuntu.com/ubuntu xenial-updates/multiverse all Packages
Ign:56 http://br.archive.ubuntu.com/ubuntu xenial-updates/multiverse Translation-en
Ign:57 http://br.archive.ubuntu.com/ubuntu xenial-backports/main amd64 Packages
Ign:58 http://br.archive.ubuntu.com/ubuntu xenial-backports/main i386 Packages
Ign:59 http://br.archive.ubuntu.com/ubuntu xenial-backports/main all Packages
Ign:60 http://br.archive.ubuntu.com/ubuntu xenial-backports/main Translation-en
Ign:61 http://br.archive.ubuntu.com/ubuntu xenial-backports/restricted amd64 Packages
Ign:62 http://br.archive.ubuntu.com/ubuntu xenial-backports/restricted i386 Packages
Ign:63 http://br.archive.ubuntu.com/ubuntu xenial-backports/restricted all Packages
Ign:64 http://br.archive.ubuntu.com/ubuntu xenial-backports/restricted Translation-en
Ign:65 http://br.archive.ubuntu.com/ubuntu xenial-backports/universe amd64 Packages
Ign:66 http://br.archive.ubuntu.com/ubuntu xenial-backports/universe i386 Packages
Ign:67 http://br.archive.ubuntu.com/ubuntu xenial-backports/universe all Packages
Ign:68 http://br.archive.ubuntu.com/ubuntu xenial-backports/universe Translation-en
Ign:69 http://br.archive.ubuntu.com/ubuntu xenial-backports/multiverse amd64 Packages
Ign:70 http://br.archive.ubuntu.com/ubuntu xenial-backports/multiverse i386 Packages
Ign:71 http://br.archive.ubuntu.com/ubuntu xenial-backports/multiverse all Packages
Ign:72 http://br.archive.ubuntu.com/ubuntu xenial-backports/multiverse Translation-en
Err:14 http://br.archive.ubuntu.com/ubuntu xenial/main amd64 Packages
400 Bad Request [IP: 200.236.31.4 80]
Ign:16 http://br.archive.ubuntu.com/ubuntu xenial/main i386 Packages
Ign:19 http://br.archive.ubuntu.com/ubuntu xenial/main all Packages
Ign:21 http://br.archive.ubuntu.com/ubuntu xenial/main Translation-en
Ign:23 http://br.archive.ubuntu.com/ubuntu xenial/restricted amd64 Packages
Ign:25 http://br.archive.ubuntu.com/ubuntu xenial/restricted i386 Packages
Ign:27 http://br.archive.ubuntu.com/ubuntu xenial/restricted all Packages
Ign:29 http://br.archive.ubuntu.com/ubuntu xenial/restricted Translation-en
Ign:31 http://br.archive.ubuntu.com/ubuntu xenial/universe amd64 Packages
Ign:33 http://br.archive.ubuntu.com/ubuntu xenial/universe i386 Packages
Ign:35 http://br.archive.ubuntu.com/ubuntu xenial/universe all Packages
Err:41 http://br.archive.ubuntu.com/ubuntu xenial-updates/main amd64 Packages
400 Bad Request [IP: 200.236.31.4 80]
Ign:42 http://br.archive.ubuntu.com/ubuntu xenial-updates/main i386 Packages
Ign:43 http://br.archive.ubuntu.com/ubuntu xenial-updates/main all Packages
Ign:44 http://br.archive.ubuntu.com/ubuntu xenial-updates/main Translation-en
Ign:45 http://br.archive.ubuntu.com/ubuntu xenial-updates/restricted amd64 Packages
Ign:46 http://br.archive.ubuntu.com/ubuntu xenial-updates/restricted i386 Packages
Ign:47 http://br.archive.ubuntu.com/ubuntu xenial-updates/restricted all Packages
Ign:48 http://br.archive.ubuntu.com/ubuntu xenial-updates/restricted Translation-en
Ign:49 http://br.archive.ubuntu.com/ubuntu xenial-updates/universe amd64 Packages
Ign:50 http://br.archive.ubuntu.com/ubuntu xenial-updates/universe i386 Packages
Ign:51 http://br.archive.ubuntu.com/ubuntu xenial-updates/universe all Packages
Err:57 http://br.archive.ubuntu.com/ubuntu xenial-backports/main amd64 Packages
400 Bad Request [IP: 200.236.31.4 80]
Ign:58 http://br.archive.ubuntu.com/ubuntu xenial-backports/main i386 Packages
Ign:59 http://br.archive.ubuntu.com/ubuntu xenial-backports/main all Packages
Ign:60 http://br.archive.ubuntu.com/ubuntu xenial-backports/main Translation-en
Ign:61 http://br.archive.ubuntu.com/ubuntu xenial-backports/restricted amd64 Packages
Ign:62 http://br.archive.ubuntu.com/ubuntu xenial-backports/restricted i386 Packages
Ign:63 http://br.archive.ubuntu.com/ubuntu xenial-backports/restricted all Packages
Ign:64 http://br.archive.ubuntu.com/ubuntu xenial-backports/restricted Translation-en
Ign:65 http://br.archive.ubuntu.com/ubuntu xenial-backports/universe amd64 Packages
Ign:66 http://br.archive.ubuntu.com/ubuntu xenial-backports/universe i386 Packages
Ign:67 http://br.archive.ubuntu.com/ubuntu xenial-backports/universe all Packages
Reading package lists...

Conto com a ajuda da comunidade!

Tem um tutorial de como instalar o MySQL no Ubuntu aqui: http://www.alastori.com.br/2016/02/instalacao-mysql-57-no-ubuntu-1510.html . Veja se ajuda.

O MariaDB não serve para as tuas finalidades?

Estou achando que os servidores BR do Ubuntu estão offline.