If you are referring to the categories from the post type `post` (the blog) then this would do the trick:

[wp_list_categories()][1]

> `child_of`  
> Only display categories that are children of the category
> identified by this parameter. There is no default for this parameter.


    <?php 
      // Put the parent category ID in place of 9999
      wp_list_categories('child_of=9999'); 
    ?>



  [1]: http://codex.wordpress.org/Template_Tags/wp_list_categories