To make such a calculation, you start by making a list of cost factors and find out the weekly costs for each of them:
costs for your networking provider
the hardware (renting price, or purchasing price divided by deprecation period, broken down to a price/week), including backup systems, backup storage systems etc.
costs for any software required to run the system (per week, like above)
costs for the personal running and maintaining the system, the software and the hardware
costs for the rooms where the servers are placed
costs for the electricity, backup tapes etc.
maybe some things I forgot to mention.
Now you need to analyse how each of these cost factors would reduce in case your company would - hypothetically - not offer the service any more (or "outsource" the service to a 3rd party).
The difference is the "total costs of ownership"/week of the service. Divide that by 750 millions, and you have the costs per API request.