Do you have photos of the insect itself?  There are insect that bury items but these holes seem pretty big.  Also the holes generally would be filled in afterwards.

Thank you for your reply.  What is strange is I don’t see any insects present.  Even if I dig into one of the holes I don’t see anything.  They are just such perfectly made holes.  These are at my mothers house who lives in Littleton.  I live about 20 minutes from her but don’t have anything like that in my yard.  She has two huge ash trees in the front yard: when I check the tree leaves for insects I don’t see anything.  

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If you do see some sign of insect activity, get a photo and I'll try to give you a better idea of what's going on.  For the moment, however, I'm fairly certain that insects are not involved.