Update Drupal core via Drush

- Activate maintenance mode

drush state-set system.maintenance_mode 1

- Clear the cache

drush cache-rebuild

- Update the Files : please choose one of the below options

    - Update Drupal 8 core
           drush pm-update drupal

    - Update a single module
          drush pm-update module_name

    - Update only security updates
         drush pm-update --security-only

- Update database, if any required database updates are needed

drush updatedb

- Deactivate maintenance mode

drush state-set system.maintenance_mode 0

- Clear the cache again

drush cache-rebuild

- Done. You have successfully updated your Drupal 8 using Drush :)
 

Reference : https://www.drupal.org/docs/8/update/update-core-via-drush