Is cycling my tank with 8 Zebra Dano's sufficiant?

the only real way to know would be to test your water. It depends on your set-up, how much you're feeding, any ferts for plants, water additives, and etc. Sounds like you're off to a good start though.

Well it will be good if you plan on keeping 8 danios in the tank. The bacteria will grow to the level of the food available. 8 danios will produce 8 danios worht of food. Add more fish and your bacteria will need to grow to compenaste, thus require another bump in the cycle of the tank. Each time you add a fish in additon this will occur. The live plants will off set things a bit but testing the water is the only way to keep track of things.

Also while danios are considered hardy fish, they are still suceptable to damage from ammonia and nitrite levels. Thus testing and water changes are the only way to keep levels to a tolerable level.

And finally you will now have 8 danios in your tank. Is that the kind of fish you wanted? Don't buy fish unless they are the kind you actiually want, regardless of fish store advice.