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How can I display the all children of a child page?

I'm using the below to list all child pages of the current parent page. I now need to list and child of the children pages... That may be confusing..

Get current page ID > Display all direct children of that page ID > I now need to also display the current pages children's children...

So like:

• Child page
• Child of Child page
• Child of Child page
• Child page

<div class="nav-col">
    <?php 
    global $post;
    $direct_parent = $post->post_parent;
    ?>
    <div class="side-nav">
    <?php 
    wp_list_pages(array(
        'child_of'    => $direct_parent,
        'title_li' => ""
    ));
    ?>
    </div>
</div>