I have a basic problem (I guess). I'm just using the default cube, I added a material then a texture I chose the default "marble" pattern. When I render it, it looks like it should. However, when I export the object (tried all different formats), then import the model back into blender, there is no marble pattern on the cube.
Other formats than blenders .blend don't support Blenders full feature set, have different settings or similar functions, which are not always compatible. Not all Settings, Materials or Datatypes are saved by export functions. So if you don't want to import your model in a different Program, use the
Save As Function to save your file in the native .blend format.
maybe try to "pack external data"?
File ‣ External Data ‣ Pack into blend-file