If you want to remove the heading from either a left or right sidebox you can just do the following and you don't need to create extra files or do anything else:
1. Edit the tpl_box_default_left.php or tpl_box_default_right.php (depending on which side you want to place the banner box) from the \includes\templates\YOUR_TEMPLATE\common\ directory.
2. For tpl_box_default_left.php replace everything between
<!--// bof: <?php echo $box_id; ?> //-->
and
<!--// eof: <?php echo $box_id; ?> //-->
with:
<?php if ($box_id == "bannerbox")
{ echo $content;
} else {?>
<div class="leftBoxContainer" id="<?php echo str_replace('_', '-', $box_id ); ?>" style="width: <?php echo $column_width; ?>">
<div class="sidebox-header-left <?php echo $header_left; ?>">
<h3 class="leftBoxHeading <?php echo $header_right; ?>" id="<?php echo str_replace('_', '-', $box_id) . 'Heading'; ?>"><?php echo $title; ?></h3>
</div>
<?php echo $content; ?>
</div>
<?php } ?>
3. For tpl_box_default_right.php replace everything between
<!--// bof: <?php echo $box_id; ?> //-->
and
<!--// eof: <?php echo $box_id; ?> //-->
with:
<?php if ($box_id == "bannerbox")
{ echo $content;
} else {?>
<div class="rightBoxContainer" id="<?php echo str_replace('_', '-', $box_id ); ?>" style="width: <?php echo $column_width; ?>">
<div class="sidebox-header-left"><h3 class="rightBoxHeading" id="<?php echo str_replace('_', '-', $box_id) . 'Heading'; ?>"><?php echo $title; ?></h3></div>
<?php echo $content; ?>
</div>
<?php } ?>