Are you sure its the cooler and not a leak in a line or connector ?
If you are unsure you could pressure test the cooler, if you are not sure how to do this or don't have the tools any radiator repair shop should be able to do it for you and affect repairs as required.
It would be odd if old oil damaged the cooler more likely external factors, or perhaps an over pressure problem due to a blockage somewhere in the system, once you get the leak sorted get the pressure tested after you do the oil and filter.
Its not the destination that is important its the journey.
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