Maybe make 2 quite thin layers of cake and sandwich between them some low joule jelly, custard, cream etc so that there's less carbs and it's lower gi. Ice cream cake would probably be better also. Ice with cream instead of icing, strawberries and berries dont affect blood sugar so that would make a nice topping. Yo could also look at flour less cake made with almond meal, nuts are great, flour not so great and those cakes are very rich so a small portion would do
For a regular cake I him a sponge would probably be best as its light, higher I protein because of all the eggs and lends itself to being filled and topped with cream or custard etc.
Strawberries and berries don't affect blood sugar? Um, yes they do!
Just ask mum what the guidelines are and what he likes! Chances are they have decided to let him have a little splurge on his birthday and will allow him to eat a small piece of anything, and then adjust with extra insulin. The refined flour in the cake will cause as much a blood sugar rise as the sugar. There is no such thing as cake that is 'good' for a diabetic, type 1 or type 2 (incidentally to the PP who said type 2 diabetics have to avoid all sugar - that's wrong too - it depends why they are diabetic and what meds they are on including if they need insulin or not).
A chocolate cake with white flour and icing really isn't that much worse than a nut cake with cream and strawberries; one way or another extra insulin will be needed. So make the poor kid a cake he actually likes - if they are going to the effort of letting him have a special day and managing it with extra blood tests and insulin, at least let that effort be for something he loves, rather than a sugar free flour free icky version of a cake!
But no one on this forum can answer the question, OP, because it all comes down to the parents plan of how to manage the diabetes on the day. Of they want a sugar free flour free cake, that's fine. But if they want to just let him have what 'normal food' he wants and give him extra insulin, that's fine too. Just ask mum what he would like and what you are and aren't allowed to use! And if he says to make him a 'normal' cake don't be too surprised!