Problem: Create a cron job to export posts to a WordPress XML file on server

Your problem is that ob_file ain’t global. You only define it in c3m_export_xml(). Setting global $ob_file in ob_file_callback() gives you an empty file handle. Try this instead:

function c3m_export_xml() {     
    $args=array(
        'content' => 'posts',
        'start_date' => 'october 2008',
        'status' => 'published');

    ob_start();
    export_wp($args);
    $xml = ob_get_clean();

    file_put_contents('server_path_to_my_file.xml', $xml);
}