Here's what I did for DS's birthday cake:

Goat's butter melted in microwave
Add butter, 3 eggs, 6 spoons sugar (should be honey but DH ate it all), 8 spoons self-raising flour, 3 bananas in smallish pieces to a blender.

Blend.
Into loaf tin.
In oven for 25 minutes.

Make pink icing and plonk on top once cake is baked.

TBH, any cake is quick to make in a blender! Nigella Lawson swears by it and that's how she bakes a cake most days, apparently. BTW, I checked with Nursery for allergies first. Only DS is allergic so I only had to cater for him! Other mums either don't do anything special for DS (not a problem!) or buy some dairy and nut free jam tarts or something like that for him (and God bless the mummy who did that!).