AI'm from Scotland and am a member of a baking club, our next meeting we have, to make something traditional to another country, I wondered if anyone would have any ideas of something I could bake from where you live, obviously nothing from the UK :-)
I'm partial to the Norwegian Wedding cake (kransekake; also used on other special occasions) made with almond paste. It's easiest with the correct pans, but it can be made by hand-making various lengths of "snakes."
Also, German chocolate cake is an American invention. Some people use both buttercream and the traditional coconut-pecan gooey topping. I prefer it without buttercream.
Black Forest cherry cake is German, a.k.a. Schwartzwalder Kirschtorte.
Cheesecake is not a typical kind of cake, but U.S.-ians make it a lot. Do you make it in Scotland?
Then there's the Australian (and probably elsewhere) Pavlova (meringue). I suppose that's not really a cake, but it is a delicious fancy dessert.
HTH
Does it have to be a cake?
You could make Nanaimo Bars. Definitely Canadian. 
Lamingtons an Australian treat. Lamingtons are very popular in Australia and consist of a small square (cube) of white cake (sponge, butter, or pound) that is dipped in a sweet chocolate icing (frosting) and then rolled in desiccated (unsweetened) coconut. I suspect their namesake, Lord Lamington (Governor of Queensland from 1896 - 190l), might be surprised at how popular these cakes have become. I am told that Lamingtons are sold in most Australian bakeries and sell very quickly at bake sales
Read more: http://www.joyofbaking.com/Lamingtons.html#ixzz2RQxzE6qS
Mmmm, I love lamingtons! It's usually made with sponge cake, the chocolate icing used is a runny ganache (use it straight after making instead of leaving it to firm up), but depending on where you are the desiccated coconut can be difficult to get hold of. So good! 
AYou can make all colour Lamingtons. My families favorite ( and I'm an Aussie) are pink Lamingtons. Probably because I have daughters. I make a gel out of raspberry or cranberry juice and wait till it sets to a colloidal point then dip your cake squares or whatever into the red then roll in coconut. Refrigerate for a little to let the coating stick then cut in half and cream & pop back together . Mmmmmmm. Cream in the middle is just an option some put jam as well. My daughters remember their Birthdays where I had a whole variety of colours. Chocolate is the traditional though. A fairly thin chocolate syrup. Then coconut. Oh. Now I am hungry. :-)
Mmmmm......lamingtons. Sponge is the traditional cake to make lamingtons with, but it's best to make them with day old sponge cake, otherwise it's too fresh and absorbs the chocolate rather than being coated in it. Also, it can break apart easily. Some people use butter cake for this reason.
AUbe cake from the Philippines. http://blog.junbelen.com/2010/05/25/purple-yam-why-filipinos-love-purple-sweet-treats/
AMedovik is one of the most popular cakes in Russia. It is also known as Honey or medoviy cake. It’s... - http://pinterest.com/pin/337066353330915076/
A honey cake from Russia
dobostorta with hazelnuts is amazing!
It was my birthday cake growing up, and my favourite to this day. It's more work than a typical cake, but so worth it!
It's made up of thin layers of sponge, with a very rich chocolate buttercream, (almost a ganache texture/taste) and topped with crunchy caramel.
There are more modern versions with only 5-6 layers, and soaking the top layer of sponge in caramel and precutting it into a fan, (much easier to serve,) Joe Pastry has a good one on his blog.
Ours had about 20 layers, of paper thing sponge, and covered in hard caramel. The funnest bit was cracking it with the back of a spoon, like a giant creme brulee, lol.
AI was going to suggest Kransekake too. I made my first one about a month ago for my friend's birthday and it was a lot easier than I thought it would be! You can also make it in advance as it needs to be frozen as part of the process. It tasted lovely (a bit like dry farleys rusks -though more chewy - if you remember them?). Lakeland sell a Kransekake pan. That's where I got mine. There is a pic of the cake in one of my albums (on my mobile so can't insert image). I made the Norwegian flags from edible printed rice paper and cocktail sticks.
I'm partial to the Norwegian Wedding cake (kransekake; also used on other special occasions)
It's rare I see references to my country here, so forgive me for nitpicking: But kransekake is not a wedding cake - it would be made for things like christenings and other large celebrations - but I've never ever heard of anyone who's used kransekake as a wedding cake. FYI :-)
Sachertorte, filled with apricot-jam, even though I'm not Austrian :-)
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