Remove the frozen ice and carefully rinse it in cold fresh water, say just above 0 C. so you don't melt the ice very much. Rinse it several times with new fresh cold water then taste the ice cube and compare that taste to the taste of the original salt solution. These are fresh water, as the ice from which they come accumulated on land as snowfall piled on year after year. The iceberg is extremely dense ice, sometimes with snow on top. The salt sea water does not mix with the fresh water ice that the iceberg is made of.
True icebergs are galcier fragments that have fallen into the sea.
Glaciers are made of compacted smow, which is fresh water. This is because when saltwater freezes, it excludes salt from the ice crystal lattice. You can test this out yourself in your freezer. Put some saltwater in a pan and place it in your freezer. When some of the water is frozen, skim it out , rinse it with cold water to remove any liquid saltwater on it, and let it melt.