This is an enormously difficult question to answer. There are simply too many variables at play to arrive at anything like an absolutely correct answer.

Where would you begin calculating? The cost to train and equip the soldiers involved? Their wages from the time of enlistment/conscription through to the end of the battle? Food, ammunition, and other supplies expended during the course of the fighting? The cost of subsequent medical care of the wounded? The cost of replacing men killed or wounded in the battle, and repairing and replacing broken or lost equipment?

I'm sorry to not be of more help, but this is the kind of thing that a graduate student could spend months researching.