Preheat the oven to 180 degrees Celsius (350 Fahrenheit).
To make the sponge, add the soften butter and sugar to a large bowl, and use a hand mixer to cream them together until smooth and silky.
Add the eggs one by one, beating well after each addition.
Sift in the flour, add the baking powder, coconut rum, desiccated coconut and lime zest, and use a spatula to combine all the ingredients together.
Butter and flour a loaf tin, and add the batter, spreading it evenly.
Bake for 35 minutes or until a skewer inserted in the middle comes out clean.
To make the drizzle, combine the lime zest with the sugar, and pour it over the cake as soon as it comes out of the oven.
Leave the cake to cool down completely, then use a sharp knife to run it around the edges of the cake, it should come out of the tin easily.
Sprinkle more desiccated coconut over.