I think you have done some things backwards with regards to JFrame and JPanel.
Here is some source code, that is pretty much identical to what you are doing, with some refactored/renamed elements
Specifically with GamePanel.java and Main.java, similiar to your Core_Main and Core_Windowhttp://www.thejavahub.net/thejavahub/index.php?topic=266.0
It should show you whats gone wrong.
The issue isn't with doubleBufferImage = createImage or the null gameRender() part
It lies in a deeper and broader issue with how you have your entire program setup.
Specifically you are creating a JFrame inside your JPanel, when it should be the other way around. The public static void main
should be in your JFrame, not in your JPanelhttp://www.youtube.com/watch?v=zSkHp7xQxEM
You can follow along as they write most of what you have there, pay special attention to things that are different.
Ignore the areas outside of the JFrame and JPanel class, specifically with rendering and basic setup
I got it working with the code, however it requires a lot of various small changes in Core_Main and Core_Window that'd just be a pain to most here, but those 2 links should get you going without too much difficulty.