ざっくりですが、こんなかんじかなと。
<?php
$parents = get_categories(array('parent' => 0, 'hide_empty' => false));
foreach ($parents as $parent){
echo "■{$parent->name}<br />"; // 親カテゴリ
$children = get_categories(array('parent' => $parent->term_id, 'hide_empty' => false));
foreach($children as $child){
echo "・{$child->name}<br />"; // 子カテゴリ
$child_posts = get_posts(array('posts_per_page' => 2, 'category' => $child->term_id));
foreach ($child_posts as $child_post) {
echo $child_post->post_title;
}
}
}
?>