I answered to this with an indefinite "a ...cake" . But of course, in the original there was the definite article. This sort of mistakes happen often, and the reason to that is the lack of context. Especially in situations where Spanish require the article but English don't - and vice versa, the problem becomes worse. Sometimes, I've noticed, some colloquial expression is taken as "the correct answer", and the correct answer is rejected. That gives at times a bitter taste " en mi lengua"
This explains why the imperfect subjunctive is being used as opposed to the conditional: https://spanish.stackexchange.com/questions/23670/why-is-imperfect-subjunctive-used-for-polite-request
What is the different between: "Quisiera el pastel...." and "me gustaria el pastel...."
quisiera and me gustaría are both used in similar ways and both can often me translated as "I would like" in English. I have read that there a significant regional differences in the actual use of the two. I've heard some Spaniards say that me gustaría is generally reserved for distant dreams or wishes while quisiera is often used as the polite way of ordering in a nice restaurant. Many Latin Americas prefer me gustaría for this use.
Keep in mind, for many things it is very common to just use quiero or even "ponme" which literally means "Put to me" This is very common for example for ordering a beer. I liken it to the use of "gimme" in English. :)