Bake at 350?F until golden brown, 30 to 60 minutes depending on the oven.
Insert a toothpick to check doneness. If it comes out clean, remove cake from oven.
For the Icing:
Put the coconut milk, sugar and grated coconut in a saucepan, stirring occasionally. Bring to a boil, let it cool a bit, then pour over hot cake. The icing mixture will look like condensed milk when done.