If one knows that he is about to eat bread (which constitutes a meal), he should, in most circumstances, avoid eating right before the meal those foods that do not require a beracha during the meal.[1] The reason is that one should not superfluously create a situation where he makes an extra beracha. The exceptions to this rule are beyond our present scope.[2]
Your question, however, is about a case where one has already eaten food prior to the meal. Let us begin with some background information. Reciting Birkat HaMazon exempts one from reciting the beracha acharona for food that is eaten in the midst of a meal that includes bread. Does Birkat HaMazon also work b’di’eved (after the fact) for foods eaten without bread? Rishonim infer from different gemarot that one who recited Birkat HaMazon on wine or dates has fulfilled his obligation b’di’eved because, since these foods are satiating foods, they constitute a meal of sorts.[3] The Shulchan Aruch[4] rules, though, that if one recited Birkat HaMazon for foods made from grains, he is not exempt and must say Al HaMichya. However, the Mishna Berura[5] points out that many poskim take issue with the Shulchan Aruch, as foods made out of grain (including cake) are no less filling than dates and wine. This should also apply when one connected the eating of cake to an ensuing meal and made Birkat HaMazon with the cake in mind.
However, the question is regarding l’chatchila (the proper course of action) in a case where one ate cake before the meal and became obligated in Al HaMichya. Why should the subsequent Birkat HaMazon, which is appropriate only b’di’eved, suffice? Indeed, if one eats spaghetti before his meal, he should make an Al HaMichya before partaking of the bread and, if he failed to do so, then he should recite it during the meal.[6] Only if he already made Birkat HaMazon would we say that he fulfilled his obligation and should not recite Al HaMichya. The Mishna Berura does cite a minority opinion that if one will be eating these same foods during the meal, then the eating of the food before and after the bread are combined into one eating experience subsumed under the meal, and Birkat HaMazon exempts l’chatchila. The Igrot Moshe[7] reasons that the Mishna Berura’s preferred opinion is to make a beracha acharona before the meal, even in that case. However, it is best to make a reasonable break between the snack and the beginning the meal. Then, it is clearly correct to end the snack with a beracha acharona before starting the meal.[8]
The matter is more complicated in the case of cake. There is a category of baked, grain products known as pat haba’a b’kisnin, for which one is required to make a beracha when he eats it as a dessert.[9] Usually, we do not make a beracha on cakes eaten at dessert because it is unclear what pat haba’a b’kisnin actually is. The Shulchan Aruch[10] cites three opinions as to the defining character of pat haba’a b’kisnin: 1) It contains a pocket of sweet filling; 2) Its dough is sweet (for Sephardim, slightly sweet; for Ashkenazim, very sweet); 3) It is thin and brittle like a cracker. Most dessert-like baked goods have one or two of these characteristics but not all. In such a case, the Bi’ur Halacha[11] says that it as a safek whether it is pat haba’a b’kisnin or bread, and we do not make a beracha because of the uncertainty. If an average piece of cake might be bread, then not only could one exempt himself b’di’eved from a beracha acharona with Birkat HaMazon, but it is likely the proper thing to do. (See also opinions of Sephardic poskim on the matter in V’Zot HaBeracha, ch. 9 – the question was asked by an Ashkenazi).
Therefore, if one eats a standard piece of cake before the meal, the Mishna Berura[12] says not to make an Al HaMichya before the meal.[13] When reciting Birkat HaMazon, it is preferable to have in mind specifically that it refers to the pre-meal cake as well.[14]