Which empire's core was germany, austria, moravia and bohemia and later grew to include switzerland, the netherlands and parts of italy, france, poland, hungary and denmark

I am not sure if there is a mistake in the question? 

The correct answer COULD BE Austria-Hungary, or in other times just "Austria" or "Austrian Empire". 
The capital of the empire was in Vienna and the most important unifying factor was the power of the Habsburgs: the Empire was composed of many ethnicities and many languages but what they had in common was the Habsburg rule. 

Austria-Hungary included parts of today's Germany, Austria, Moravia, Bohemia, the Netherlands and parts of Italy, France, Poland, whole of Hungary. However, Denmark was not part of Austria- HUngary . 

Another good candidate is the Holy Roman Empire. Here the whole of Switzerland was also included, as were Germany, Austria, Moravia, Bohemia, the Netherlands and parts of Italy, France, Poland, However, again, Denmark was not part of it and neither was Hungary. 

So in the end, the question is confused and lists some mistakes in it. 

I personally would go with Austria-Hungary, since the definition of this empire was more fluid, as in "all the lands that belong to the Habsburgs", but I feel that the question might be asking for the Holy Roman Empire (and mistakes Hungary as a part of Austria-Hungary to be a part of the Empire, which it wasn't). 

Smelly rocks sink in water haha!