Preheat oven to 160C/325F/Gas 3. You will need a greased and lined 18cm/7in round or square baking tin.
In a large bowl or electric mixer, whisk together the oil, sugar, eggs and golden syrup until totally combined. Mix in the remaining cake ingredients and pour into the prepared tin.
Bake in the oven for 45 minutes for a round cake, or 30 minutes for the square, until nicely risen and firm but springy when lightly pressed. Insert a skewer through the centre if you're not sure. If it comes out clean, the cake is ready. Leave the cake to cool in the tin for 10 minutes before turning out onto a wire rack to cool completely.
While the cake is cooling, make the topping. Warm the marmalade in a microwave or small saucepan until melted. Beat it into the cream cheese with the coconut cream and icing sugar. Place in the fridge to firm up, and when cold spread over the cooled cake.
For a final touch, grate over some nutmeg or dust with some ground cinnamon. Because the carrot cake has been made using oil, it will stay moist for quite a few days in an airtight container if you can bear not to eat it straight away.