Mix the Extra Virgin Olive Oil from Spain and the sugar in a bowl. Add the eggs, mixing them in one at a time. Then, slowly add the flour, baking powder and vanilla flavouring, stirring continuously until you get a uniform mixture.
Divide the mix into 6 containers, one for each colour. Add a dye to each and mix well so that the dye spreads uniformly through the dough.
Prepare 6 baking tins, coat them with a little Extra Virgin Olive Oil from Spainl and dust them with flour. Put each mix into a separate baking tin. The mixtures should be smooth. You can also make the sponge cakes separately if you don't have enough baking tins.
Preheat the oven to 180ºC and bake the sponge cakes at that temperature. After about 20 minutes, remove them from the oven and from the baking tins, then leave them to cool.
Separately, whip the cream with the sugar and, before it is completely stiff, add the cream cheese and stir until well mixed.
Now let's put the cake together! Put some of the icing on the base and then carefully place the red sponge cake on top. Add a thin layer of icing and then another sponge, following the colours of the rainbow. Continue until you've used all the sponges.
Cover the cake with a thicker layer of icing and leave it to stand for about 15 minutes. Now it's ready to eat!