The location of my country within Europe: 我先說一下我國在歐洲中的地理位置 I started my essay with:


  我先說一下我國在歐洲中的地理位置,⋯


Apparently, there are a lot of problems with this. It seems that the teacher thought my country was in Central Europe, since he changed 中 to 中部。I wanted to say:


  "I first talk about the geographical location of my country within Europe." 


Should I have used 內 or 裡？
Your first try is a correct translation of the English you want to say. 内 or 里 are not as good as 中. 

Better still, you can omit it, 我國在歐洲的地理位置. Here "in" is implied.

After your teacher's modification

我先說一下我國在 歐洲中部 的地理位置 = I first talk about the geographical location of my country in Central Europe. (Here 歐洲中部 means Central Europe and "in" is implied. Notice the change in sentence structure.)

user6065's suggestion 我国在欧洲里占有的地理位置 isn't good. If you say that, people will expect you to immediately follow that your country's location is strategically important (which may or may not be what you want, but certainly not reflected in your English expression).