Is in Drupal the way to cache whole region?
Rather cache the individual blocks. There is a module for that: Block Cache Alter


  Alter cache settings per block. Cache settings per block are now set
  in code, but if you don't like the default - usually none - you can
  now easily change this. Install this to speed up block rendering for
  authenticated users.


It will give you the optioon in the Block UI to alter the cache settings for that block: