Gofer,
I have an Excel table listing ICAO Codes, IATA Codes and airport name. It can be searched or sorted by any of those categories to get the other two.
I got it with charge calculation software from from the Central Route Charges Office (Eurocontrol) website, some years ago. There may be an up-to-date version there now.
It has 7781 entries, not all with both ICAO and IATA codes, of course.
PM if you want a copy.