Yes, cycling a tank usually takes 3 - 4 weeks or more.
You would be wise to remove the clowns; they are in danger from ammonia/nitrite poisoning and use a blue damsel or even just a cocktail shrimp instead. Before you start adding anything as delicate as corals you might want to slow down & do a lot of research with a good book or two and make sure you understand the cycling process, filtration and lighting options, etc. before moving forward, afterward it would be a good idea for you to stick with marine fish for a year or so before trying corals.
Your research will lead to success.