Which sideboxes are you referring to? There are some that are for products, ie: New, Featured, Specials. Then there are banner boxes. If I'm understading you correctly, you probably need to use banner boxes for your purposes. Those are edited in:

public_html/includes/languages/your_template/english.php

On these lines:

define('BOX_HEADING_BANNER_BOX','Heading Here');

define('BOX_HEADING_BANNER_BOX2','Heading Here');

define('BOX_HEADING_BANNER_BOX_ALL','Heading Here');

You would simply remove the heading language and leave the two hashmarks.