Display list of Sub-Categories and the posts they contain, within one main Category

I’ve found tons of code and plugins to do various things; from show posts for specific cats, subcats of a cat, etc.. BUT, I cannot for the life of me find, nor do I know the WP API well enough to do what I need with it..

Here is what I’m trying to accomplish:

Display a UL of all subcats within Cat31, and the posts for each of those subcats:

• SubCat1

  • Post 1
  • Post 2

• SubCat2

  • Post 1
  • Post 2

• SubCat3

  • Post 1
  • Post 2

It’s pretty straight forward, but all the loops I have tried fail either at the subcat loop or the post loop (one or the other works, I cannot get them both to work..)

So, unless I can find a plugin to do this (I’d prefer to code this into a template file!) then I need to figure out how to:

Loop Subcats within Cat31 while looping subcasts, loop posts for each subcat

Any help is GREATLY appreciated!

Question was answered on another site.. thank you!
BTW, the code that accomplished what I needed was:

$categories =  get_categories('child_of=31');  
foreach  ($categories as $category) {
    //Display the sub category information using $category values like $category->cat_name
    echo '<h2>'.$category->name.'</h2>';
    echo '<ul>';

    foreach (get_posts('cat=".$category->term_id) as $post) {
        setup_postdata( $post );
        echo "<li><a href="'.get_permalink($post->ID).'">'.get_the_title().'</a></li>';   
    }  
    echo '</ul>';
}