Preheat oven at 355 F. Butter a round cake pan (9-inches diameter) well. Evenly sprinkle the cane sugar. Set aside.
Trim the strawberries and cut them in half.
Cover the whole pan with the cut strawberries. Place the cut strawberries face down in a circle on the bottom with the largest part of the strawberry against the rim.
In a small bowl, mix coconut, all-purpose flour, and baking powder.
Beat the butter and sugar with a stand or hand mixer until well-combined and the mixture becomes creamy.
Add the eggs one at a time, scraping down the sides of the bowl and beating well after each addition.
Mix in the flour mixture just enough to blend the flour (do not overmix). Scrape the bowl if needed.
Cover the strawberries with the batter. Use a spoon to evenly spread the batter.
Bake in the oven for 35 minutes or until a toothpick inserted in the center comes out clean.
Meanwhile, in a small bowl mix the coconut and sugar. Toast until lightly brown in a small skillet. Add the lime zest, mix, and set aside.
Before removing the cake from the mold, let it cool for 15-20 minutes on a wire rack. Run a knife around the edges of the pan and place a serving dish or plate on top. Invert the cake onto the serving dish and carefully remove the pan.
Let the cake completely cool down before sprinkling the coconut all over the cake and slicing.