Since the initiation of the game, the statistics of castles have changed and I believe the following is now an accurate description of the way they work.

Castles used to give you, individually, a 10% defense bonus that was cumulative, so it used to work out like this;

1 Castle = 10%
2 Castles = 20%
3 Castles = 30%
4 Castles = 40%
and so on.

Now the formula has been altered to provide a fairer system for lower ranking kingdoms:

SQRT(Castles)*10 = % defence bonus, so;

1 Castle SQRT(1)*10 = 10%
4 Castles SQRT(4) = 2*10 = 20%
12 Castles SQRT(12) = 3*10 = 30%
16 Castles SQRT(16) = 4*10 = 40%
and so on.