Preheat the oven to 200C/180C Fan/Gas 6. Grease and line 5 x 20cm round sandwich tins.
Put 400g of the sugar, the Best for Baking Cakes, flour and baking powder into a large bowl. Crack in 5 of the eggs and add the milk
Beat with an electric whisk until fluffy. Divide into 5 bowls. Add 1⁄2 tube of blue food gel to one, then repeat with the other colours. Mix gently until coloured evenly.
Spoon each batter into a separate cake tin and level the tops. Bake for 18-20 mins until a skewer inserted comes out clean. Cool fully on wire racks.
Meanwhile, reduce the oven to 140C/120C Fan/ Gas 2. Line 2 baking trays with baking paper.
Separate the remaining 2 eggs and put the whites in a large, clean bowl (save the yolks for another recipe). Beat with an electric whisk until soft peaks form. Beat in the remaining 100g sugar, a spoonful at a time, until incorporated, then beat on high until thick and glossy.
As shown in the images below, using a clean, wet paint brush, paint stripes of each colour of food gel up the inside of a large piping bag. Put the meringue in the bag. Cut off a 2cm hole at the end and pipe 18 meringue ‘kisses’ onto the trays. Bake for 30 mins then turn down to 120C/100C Fan/Gas 1 and bake for a further 45 mins. Leave to cool.
To assemble, sandwich the layers together with frosting, starting with the blue cake on the bottom, then green, yellow, orange and red. Coat the outside in a thin layer of frosting and chill for 30 mins.
Reserve some frosting for the top of the cake then divide the rest between 5 bowls. Use 1⁄2 tube of each food gel to colour each one. Divide into 5 piping bags then cut off each bag 2cm from the tip. Pipe a 2cm-deep line of each icing around the cake, starting with blue on the bottom.
Smooth with a cake scraper or palette knife.
Ice the top of the cake with the reserved frosting. Top with the meringues just before serving.