I dont think food could be producing nitrate through any process other than the nitrogen cycle.
As you are feeding the cycle with fish food rather than ammonia or ammonium chloride you have no way of knowing how much ammonia is being processed apart from making presumptions based on how much nitrate you are producing.
8ppm would result from about 2ppm ammonia, so based on that you are cycling out about 0.6ppm ammonia per day. But, the test kit won't be so accurate to know exactly how much nitrate you have. All you can really say is that you have a low to moderate level of nitrate production over 3 days.
Also the bio support you added went into the water column and will have acted on the ammonia from there and may or may not have established on your filter media. 3 days of nitrate production is not long enough to tell if the beneficial bacteria has established properly.
All you can really say is that you likely have some cycle, which is better than none. In your situation i would do a big water change prior to adding your fish, make sure you get out all the waste food you added, add some more bio-support, and proceed as you would with a fish on cycle.