Here is a working example that I've tried with Literal control as
F-ES Sitecore suggested.
Your aspx page
<div>
<asp:Panel ID="Panel1" runat="server"></asp:Panel>
</div>
Your code behind
var videoFrame = new Literal();
videoFrame.Text = string.Format(@"<iframe width=""628"" height=""374"" src=""{0}"" frameborder=""0"" allowfullscreen></iframe>", "https://www.youtube.com/embed/9bi9eDZUJPQ");
Panel1.Controls.Add(videoFrame);