There is a traditional madeiran cake, which is called 'Bolo de Mel' - honey cake.
There's no honey in it. Well, no bee-honey, but it contains sugar-cane 'honey'. The cake isn't golden and light, but dark and heavy. Worst of all, it has nuts in it. Gakkarama.
Other people like it though.
As for what the rest of the world calls madeira cake: they've never heard of it here. Now there's a niche market waiting to be exploited: sell tourists the cake that they expect to find. I can see it now: the madeira cake wars...