Now that things have settled down a bit, I'd like to offer some suggestions. First though, please do not jump into things; I know myself how tempting it is, especially when starting out with a new tank, to think this or that is not "as it should be" and into the tank goes this or that chemical to "fix" it. No. That is the absolute worst thing you can do with live fish in an aquarium. The effect of some chemicals or substances on bacteria, water parameters, and the biological system can be immense, and in a closed system the fish are trapped in this mess. I'm not saying you have a mess, just a general caution not to hurl yourself into a solution. If the tank is relatively stable biologically speaking, the fish will be far less stressed and thus healthier, than if the water is fluctuating back and forth with this and that.
Nitrates. This is the third stage in the nitrification cycle. Fish and bacteria (different types, these in the substrate) produce ammonia, nitrosomonas bacteria consume the ammonia and produce nitrite, and nitrospira bacteria consume the nitrite and produce nitrate. Ammonia, nitrite and nitrate are all forms of nitrogen; ammonia and nitrite are highly toxic, nitrate much less so. However, fish in natural waters do not have to contend with nitrates, generally speaking, so any level of nitrate can be troublesome to some degree for many fish. Most of us recommend nitrates be below 20ppm, though up to 40ppm is tolerable for most of the "common" fish. While it can be debated that even higher nitrates are not an issue, there is no argument that some fish find difficulty with higher nitrates, so it is wise to keep them at or below 20ppm.
As your tap water has zero nitrate, the nitrates in the aquarium are from within the aquarium. There are two major ways to naturally control nitrates. One is with live plants, the other is with regular partial water changes. Live plants use ammonia directly (which they change to ammonium, their preferred form of nitrogen) and with lots of live plants and a balanced fish load, you will absolutely never have nitrates above 20ppm, usually well below 10ppm. A certain benefit of live plants.
Water changes are essential to a healthy aquarium, unless it is lightly stocked with fish and heavily planted, in which case the natural biological equilibrium will be stable. But most of us like more fish, so the weekly water change is crucial to the fish's health. However, along with this, if nitrates continue to be high even with water changes, it probably means there is something amiss with the biological system. Too many fish for the water volume, too much feeding, or too few water changes.
Last comment on Nutrafin's Cycle. This is a chemical mix that supposedly jump-starts the nitrifying bacteria. I used it many years ago when I had to pull my tank down and reset it, but normally I have live plants so "cycling" is not an issue. Rather than Cycle, I would use a true 100% bacteria supplement. I know of two, Seachem's Stability and Tetra's SafeStart. I won't get into the scientific munbo-jumbo now, but these two are 100% live bacteria and they do work. But they are only needed during the first week, to "seed" the bacteria. So, on the Cycle, I would not continue using it.
I hope this has explained things a bit for you. Feel free to ask questions.