After doing a lot of research online about what might have gotten the eggs, I feel my cat was not the one guilty.
I am going to make a new house and get it very properly constructed before putting it out for my Bluebirds. Have lots of information now from those who are all about helping the Blues.
My cats are 'farm workers', during the day they spend time keeping rodents under control and spend the night in my garage for their own protection. I do have raccoons because of the crops that are planted and also am near wetlands.
Do not know if snakes are a problem as I have not seen them but will snake proof the new house.
So your information got me going, to go deeper and find the correct solutions.
Thank you