It may take several weeks for a tank to become fully cycled. The best way to tell is check your ammonia and nitrIte levels. If these remain at 0 for at least a week or 2, then you should be good. This is of course, assuming the tank is filled with the fish that you intend to stock with.
Once your tank has the proper amount of fish for the size of the tank and is running for several months without any fluctuations in ammonia or nitrIte levels, then you can say your tank is established.
Once your tank has the proper amount of fish for the size of the tank and is running for several months without any fluctuations in ammonia or nitrIte levels, then you can say your tank is established.