What are the cubic formations found inside Larimar gemstones?
Calcite and hematite may not be the the answer to my question


Hematite is not the answer, but calcite is.

The inclusions are not cubic, they are rhombohedral. This is precisely how calcite looks like.


  but why they stand out from the rest of the stone is beyond me. 


Because calcite is a translucent mineral, and pectolite is not. You can drop some vinegar on the inclusions and you will see that they fizz a bit - this is how calcite reacts to acid.

You can read this for some more information:

http://www.openaccessjournals.siftdesk.org/articles/full-text/X-ray-Photoelectron-Spectroscopy-study.html