Do you mean one cake that has three layers of cake in it? It would probably be anywhere from 4 to 6 inches tall in total.
Or three stacked cakes? This would definitely need dowels in the bottom tier (to support the middle) and the middle tier (to support the top).... you can use bubble tea straws or the plastic dowels you can buy in the craft store.
ETA: if you are doing a stacked cake, you also want to make sure the cake board (aka cake drum) is strong enough to not flex under the weight of the tiered cake. Each of the stacked cakes are built on a cardboard round that exactly matches the size of the round then you tape the bottom tier to the cake drum; etc...
