The amount of damage depends only on the number of "structures" (buildings) currently in the city (the level of defense of the attacking unit and its position on the battlefield do not affect the amount of damage, which is the case with ranged attacks by ranged units of the defenders).

"1. All "upgrades" of military buildings, the administrative building (starting with City Hall), and the Mage Guild (starting with the second level) do not increase the number of "structures," as the main building has already been constructed.
2. Additional population increases (such as Griffin Bastion - Castle, Sculptor's Wings - Tower, Miner's Guild - Rampart, etc.) are also not "structures." These "upgrades" do not even affect the appearance of the city when entering the Hall; they cannot be selected with the "mouse" and their name cannot be displayed in the "information bar."
3. The Citadel or Castle is not included in the number of such "structures," as its "towers" already inflict damage on attacking units, and much more than each "structure."
4. Some cities have other "upgrades" that are, of course, not "structures."
The formula for calculating the damage in Hit Points (HP) inflicted by the central tower of a specific city is as follows:

Damage (HP) = D + d*N, where
D is the basic level of damage inflicted by the tower - 10-15 HP
d is the additional bonus to the attack power that the ranged tower gains when building another structure - 2-3 HP
N is the number of structures that have already been built in the city"