produce= make something inside one of your production buildings
build=build something
Your quest states "produce Dwarven Statue"
A Dwarven Statue is not a cultural building, otherwise there would be a cultural building called that. You do get quests that come up requiring you to build specific cultural buildings, but those quests also tell you which building to make.
This quest is a production quest, the production it is asking you to make is located inside your copper foundry. Once you produce a Dwarven Statue from your copper foundry, the quest will accomplish.