Preheat the oven with electrical heat at 175 degrees Celsius.
Cover a baking form with removable edges with a baking paper.
Whip the eggs and the sugar white and fluffy.
Mix all the dry ingredients together and add them in the mixture.
Add the oil, buttermilk and the food coloring, and mix it all well.
Pour the batter in the baking form, and place the cake in the middle of the oven for approx 50 minutes.
Take out the cake and let it cool down.
Mix the cream cheese, lime juice and the icing sugar together to a smooth mixture.
Place the cake and the frosting in the fridge for 30 minutes.
Take out the cake and the frosting from the fridge. Divide the cake in three.
Place the first layer on a plate and evenly spread 1/3 of the frosting on top of it. Repeat the same with the second layer. Place the third layer of the cake and spread evenly the rest of the frosting on top and on the edges of the cake.
Place the cake in the fridge for minimum 2 hours before serving it.