There's not very much cyanide in apple cores, so I wouldn't worry. The chemical in question is amygdalin, a cyanogenic glycoside (basically a sugar with a -CN molecule appended). It's also contained in almonds (and anything flavoured by almonds). There are similar chemicals in cassava etc.
You'd need to eat about 15 kg of marzipan before worrying, which is a lot even by my standards.
If you routinely consume high levels of cyanide, you will start to express more enzymes that detoxify it, turning it into an amino acid that you excrete in your urine. So it's possible to train yourself to withstand cyanide poisoning, however unless you're planning to become a secret agent, it's probably not worth the effort.
(Contrary to popular belief, cyanide isn't that toxic, it's nowhere near as dangerous as hydrogen sulfide, for instance, and you get a bit guff of that from a boiled egg.)