Do I need to install Drupal using Drush in order to use Drush?
No, you do not need to install Drupal using Drush in order to use Drush. All you need is to make sure that while running drush cc all, you are in the Drupal directory.

For example, if your Drupal lies under /var/www/Projects with root name as drupal then first you need to move inside /var/www/Projects/drupal and then run the drush cc all command.

The reason being, Drush can be executed inside a Drupal environment only.