Heat oven to 180C/160C fan/gas 4. Using a double layer of foil, make a barrier down the center of a 20cm square tin (or use a Battenberg tin), then line each compartment with 2 pieces of baking parchment. Put all the cake ingredients except the food colouring in a large mixing bowl and blend with an electric hand whisk until smooth. Tip half the cake mixture into one side of the tin. Quickly mix the food colouring into the remaining cake mixture. When you have a smooth and vivid pink colour, scrape this mixture into the other side of the tin, then spread both mixtures to the edges of their sections. Bake for 25-30 mins until a skewer comes out clean. Cool in the tin for 15 mins, then transfer to a wire rack to cool completely.
Place the cakes on a chopping board and trim the sides of each one to give you a straight edge. Cut each one in half lengthways to give you 2 pink and 2 plain rectangular sponges, using a ruler if you want to be really exact. If the sponges are a little taller than they are wide, trim some sponge from the tops as well – this will ensure you have a perfect square when you come to assemble the cake.
Heat the apricot jam in a small pan or the microwave, then sieve it. Lightly dust a work surface with a little icing sugar, then roll out a quarter of the marzipan to a rectangle roughly 20 x 10cm. Brush the surface with the warm apricot jam, then place 1 plain sponge and 1 pink sponge side by side on top, brushing the middle of the cakes with a little jam to stick them together. Brush the top of the cakes with more jam, then place the remaining sponges on top, with more jam in between, in a chequerboard pattern.
Roll out the remaining marzipan to a rectangle roughly 20 x 25cm. Brush any remaining jam over the outside of the assembled cake. Using a rolling pin to help, lift the marzipan over the cake. Smooth it over the top and sides, and press gently into the corners so it wraps the cake tightly. Trim any excess marzipan about 1cm from the sides of the cake, and trim a thin slice off either end to neaten. To finish, crimp the marzipan around the base by pinching with your finger and thumb.