I personally use get_publish() function to obtain a specific publish content. However, I am unable to result in the auto embed video runs.

This is actually the code

<?php
$post_id = 110;
$queried_post = get_post($post_id);
$content = $queried_post->post_content;
$content = apply_filters('the_content', $content);
$content = str_replace(']]>', ']]&gt;', $content);
echo $content;
?>

I would like it auto identify the youtube link and let the embed video. The sample submissions are

Check out this cool video:

http://www.youtube.com/watch?v=nTDNLUzjkpg

That was a cool video.

http://codex.wordpress.org/Function_Reference/get_post

http://codex.wordpress.org/Embeds

I've not attempted this myself, but this is exactly what I will tell you:

  1. The oEmbed functionality is used in wordpress with a filter.
  2. The get_posts() function inhibits filters automatically and that i guess get_post() does exactly the same, although I wasn't in a position to verify this within the documentation.

Possibly you should use query_posts() (which does not suppress filters) or get_posts() with suppress_filters=>false to check this.