Oil cooler
That will be the oil cooler. While the EGR cooler leaking is a common problem it will not get oil in the water, just the exhaust system. Oil cooler leaks are also fairly common, I figure someday they will make a recall on em.
We have about 250 F-series superduty's with the 6.0 in our fleet and about half have had oil cooler problems, as well as EGR cooler problems.
Pretty much the same removal procedure for both problems. Remove the air intake and assorted hoses to get to them they are under the intake.
Drain enuff coolant to get below the heads for starters. The oil cooler is the square one at the front of the block.
After about 10 of them it gets pretty easy. Be carefull tightening the intake bolts they are easily broken.