Galera, o erro é o seguinte.
mysql.service - LSB: Start and stop the mysql database server daemon
Loaded: loaded (/etc/init.d/mysql)
Active: failed (Result: exit-code) since Mon 2016-05-09 15:51:15 BRT; 1min 9s ago
Process: 3562 ExecStop=/etc/init.d/mysql stop (code=exited, status=0/SUCCESS)
Process: 5626 ExecStart=/etc/init.d/mysql start (code=exited, status=1/FAILURE)
May 09 15:51:15 owncloud /etc/init.d/mysql[6529]: 0 processes alive and '/usr/bin/mysqladmin --defaults-file=/etc/mysql/debian.cnf ping' resulted in
May 09 15:51:15 owncloud /etc/init.d/mysql[6529]: [61B blob data]
May 09 15:51:15 owncloud /etc/init.d/mysql[6529]: error: 'Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)'
May 09 15:51:15 owncloud /etc/init.d/mysql[6529]: Check that mysqld is running and that the socket: '/var/run/mysqld/mysqld.sock' exists!
May 09 15:51:15 owncloud /etc/init.d/mysql[6529]:
May 09 15:51:15 owncloud mysql[5626]: Starting MySQL database server: mysqld . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . failed!
May 09 15:51:15 owncloud systemd[1]: mysql.service: control process exited, code=exited status=1
May 09 15:51:15 owncloud systemd[1]: Failed to start LSB: Start and stop the mysql database server daemon.
May 09 15:51:15 owncloud systemd[1]: Unit mysql.service entered failed state.
Também não encontro o diretório /var/data/mysql
Ja executei o comando chown -R mysql:mysql /var/lib/mysql como root