This is probably a case of apple scab development.  There is quite a bit of secondary rot caused most likely by codling moth emergence. I do not see the cracking usual with this disease, however. Were they spots on the leaves of the trees? Could you send a picture of apples cut in quarters to show the inside? I'd love to be sure of the answer.

I already ate most of the damaged apples and saved the best for last, but I did find one that had a few spots and cut it open for you. The spots go through and through the apples. This problem did not appear until after I sprayed copper on the tree a few years ago, in an attempt to prevent any disease. Since then, we have had this problem. We grafted the tree and the new grafts also have the disease.

The copper spray years ago is not a factor. The interior spots look like bitter pit, a physiological problem involving calcium uptake. The leaf spots look like apple scab mostly. I spent some time going through the references, but did not find a for positive answer of any one problem which caused both the external and internal symptoms.

Thank you Pat!

you are very welcome.