$query = "SELECT Sum(view_count) as mySum FROM videos";
$result = mysql_query($query) or die(mysql_error());
$row = mysql_fetch_array($result);
echo $row['mySum'];

SELECT SUM(view_count) FROM videos;

$result = $mysqli->query('SELECT SUM(view_count) AS sum FROM videos;');
$row = $result->fetch_assoc($result);
echo $row['sum'];

SELECT SUM(view_count) FROM videos WHERE id in (1,2)