I figured out how to make my business logo image appear in the Facebook "Like Box" and in posts without the edges getting clipped off.
Things I Tried Which Did Not Work:
The Trick: I made my profile image square then added a border of 25 pixels around the entire image. My image size before adding the border was 150x150 pixels, then after adding the border my image was 200x200 pixels. I did not try different sizes or ratios with this, so I cannot provide a proven mathematical ratio at this time, but this will get you started in the right direction without wasting too much time.