Make the sponge: preheat the oven to 160 C (140 C fan). Grease and line a 20cm square cake tin.
In a large mixing bowl, use an electric whisk to cream together the butter and sugar until light and fluffy. Add in the eggs, one at a time, followed by the yoghurt, flour and baking powder. Pour the batter into the cake tin, then bake for 40-45 minutes until a skewer comes out clean. Let the cake cool in its tin for 30 minutes, then transfer to a wire rack to cool completely.
Make the buttercream: put the butter into a large mixing bowl and use an electric whisk to beat it until it’s light and fluffy. Add in the milk and vanilla and carry on whisking for 1-2 minutes, until the liquid is fully mixed in and the butter is lighter, and paler in colour. Gradually beat in the icing sugar, then put it into a piping bag fitted with a 1 cm round tip, then leave to one side.
Make the fondant icing: put the icing sugar (minus 2 tablespoons) into a large bowl and use a spatula to gradually mix in water until it reaches the right consistency: it should leave a 1-2mm layer on the back of a spoon if you dip it in and let the icing run off. Put a few spoonfuls of the icing into a piping bag without a nozzle fitted, then separate the remaining icing between four bowls and use the food colouring gel to colour each a different pastel colour.
Assembling the cakes: trim the edges of the cake and flatten the top, then cut into 16 squares. Warm the apricot jam in a small saucepan until runny, then brush it all over the cake sides and tops and put them on a wire rack over a baking tray, well spread out. Pipe a neat 2 cm bead of buttercream on top of each cake. Spoon coloured fondant icing over each cake, helping spread it over the top and down the sides with a small palette knife. Do eight cakes in each of the 2 pastel colours, then leave to set for 30 minutes.
When the icing coating has sat for 30 minutes, snip a small hole in the end of the white fondant icing piping bag. Use it to drizzle lines over each of the cakes, then leave them to set completely in the fridge for 2 hours before serving.