Even though Green Cheeks and Suns are both called "conures" it's actually a misnomer. They are not only different species, but are actually in completely different genuses.
Sun conures belong to the genus of parrots called Aratingas. Some other commonly seen Aratinga conures are Jendays and Nandays. Green Cheek Conures belong to the genus Pyrrhura. Some other commonly seen Pyrrhura species are Crimson Bellied and Maroon Bellied conures.
The 2 types of birds aren't closely related, despite sharing the name "conure." The word "conure" doesn't actually mean anything. It's a word that aviculturists made up. In scientific papers, they're all referred to as "parakeets-"which is a very generic therm that just means "small parrot." In aviculture the word "parakeet" tends to be used for a particular species of bird (which the proper name of is budgerigar, or budgies).
Producing hybrid offspring of parrots in the same genus is both easy and usually successful because the birds are so closely genetically related. That's why you see so many types of hybrid macaws. In conures, a common hybrid is a Sunday (a sun x jenday mix).
However, producing babies from species in different genuses doesn't usually work out very well because their parents aren't sufficiently closely genetically related enough to produce healthy offspring. Genetically, a Green Cheek (family: Psittacidae, genus: pyrrhura) crossed with a Sun (family: Psittacidae, genus: aratinga) is equivalent to trying to cross a human being (family: Hominidae, genus: homo) with a chimpanzee (family: Hominidae, genus: pan). Not good.
I'm sorry to be the bearer of bad news, but almost all of these inter-genus crosses die at a young age, and the ones that do live past infancy are generally plagued with health problems. Your little guy is adorable, and i hope very much that he beats the odds and makes it.
As for your part, you need to do everything possible to keep your Green Cheek and Sun from breeding again. It's unethical to allow them to continue to produce babies that will all die horrible deaths due to genetic abnormalities.