How can I invoke Drush command inside hook_cron?
You should not call drush from inside a Drupal module.  Instead, factor out the functionality of your Drush commands into separate functions that can be called from module code and drush commandfiles alike.  Your module code should do all user access / permissions checks before calling the API functions (usually via the access checks provided by Drupal's menu system); the Drush commands should call the API functions directly, without access checks.