I would say even if you are a newbie, it will not be a tough one to generate such report. You have requested for any details about how work orders are related to cost center.
All the orders whether they are internal or work, they are linked to a specific cost center. So overall each order will have a cost center and in order to find to which cost center it is associated, you can refer to following tables: COEP or COEJ of Controlling. You can find details about cost center, order, and others over a period of time or year.
COEP has a large number of columns and can be selected while displaying data in a Web browser.
COEJ also has the same number of tables and can be selected while displaying data in a web browser:
For more details and info you can go for IW39 to extract details about work order.