Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Buildings are of three kinds:
1. If the building is for the purpose of trading, i.e. the owner wants to gain profit by selling it, then one should pay Zakah of this building. It is like trade goods, thus 2.5 percent of the value of the building should be given as Zakah.
2. If the purpose of building is to benefit only from its rent then the Zakah is due only on the rent if it reaches Nisaab and a complete lunar year passes after owning it.
3. The building is for private use and one lives in it, there is no Zakah on such building.
The above details make clear the ruling of the building you are asking about.
Allah knows best.