change custom css class to block content
You can override the template for the block.

To see what the template should be you can use the following in your themes template file.

/sites/all/themes/YOURTHEME/template.php

function YOURTHEME_preprocess_block(&amp;$vars) {
   var_dump($vars['theme_hook_suggestions']);
}


Also make sure you have a copy of block.tpl.php in your themes template folder.
You can get this by going to /modules/block/ and copying the file to /sites/all/themes/YOURTHEME/templates. 

This is handy because you can copy the code from the default block template to your custom block template and make any changes you want there. If you were to delete your custom block template it will default back.

Heres more on template (theme hook) suggestions
http://drupal.org/node/1089656