Você precisa escapar do caractere % com \
mysqldump -u 'username' -p'password' DBNAME > /home/eric/db_backup/liveDB_`date +\%Y\%m\%d_\%H\%M`.sql
mysqldump -u 'username' -p'password' DBNAME > /home/eric/db_backup/liveDB_`date +\%Y\%m\%d_\%H\%M`.sql
