tl;dr: "I will possess three cakes" means you will have three cakes. "I will have possessed three cakes" means you'll have three cakes, then later on, you won't have them anymore for some reason (you gave them away, they got eaten, etc.) The future perfect is a relative tense, which means that it places an event in reference to another event. It also embodies a sense of an action being completed—this sort of thing is called verbal aspect. Specifically, it places the completion of an event as happening after some other event. That other event is often a direct cause of the future perfect event being completed.
The future tense just means that an event happens in the future. The future perfect means that an event will happen in the future, then "conclude" in some way before a more distant future time.
In your example, "Once I make another cake, I will possess three cakes" means that sometime in the future, I will make a cake, and the number of cakes I'll have after that is three.
The sentence "Once I make another cake, I will have possessed three cakes" sounds awkward in English, because it doesn't say anything about completing the possession of three cakes. "Once I make another cake and rampaging honey badgers steal it, I will have possessed three cakes" sounds good. It gives a direct cause for the completion of your ownership of three cakes. When you use the future perfect for possessing three cakes, you're talking about a future where you had three cakes, then somehow ended your possession of those three cakes.
Your other example, "structural needs will have had a hand in shaping its form", makes more sense; it implies that the time when structural needs have a hand in shaping the building's form will be completely over and done with by the time you're referring to. You could rephrase it as "When the building's form is shaped, structural needs will have played a vital role in shaping it." Here, the event that causes the completion of the future perfect verb is implicit: "When the building's form is shaped" tells us that we're talking about a time when the building's form has already been completely shaped, and of course, when that ends, anything that plays a vital role in shaping its form will also have ended. So the end to shaping the building's form directly causes an end to the vital role played in that shaping by structural needs.
"structural needs will have a hand in shaping the building's form" just says that sometime in the future, when the building's form is being shaped, structural needs will play some part.
So the future tense really talks about events happening at just one time, which is sometime in the future. The future perfect actually talks (openly or implicitly) about two events: one in the distant future, and one in the nearer future which you expect to be completed when the distant future event takes place.
Here's another way to understand the future perfect tense: it's a time-shifted version of the past perfect. In the past tense, you could say "After I made another cake, I possessed three cakes." That would just mean that you had two cakes, made another one, and then you had three.
In the past perfect, you could say "After I made another cake and then ate it, I had possessed three cakes." The implication is strongly that the time when you possessed the cakes was over and done with before some other event that you're about to mention occurred. Similarly, the future perfect strongly implies that the event it describes happened after some other event. An event in the future perfect, like the past perfect, only really makes sense in relation to some other event that occurred after it.
Here's another example, which compares the past perfect and future perfect to show their similarities:
- "I had possessed three cars when I bought the Prius." This implies that the speaker had three cars, and was done having them at the time he bought the Prius. Another way to look at it is that the speaker really wants to talk about the Prius, but needs you to know the number of cars he had before had bought it.
- "I will have had three cars when the one I've got breaks down." This implies that the speaker currently has his third car. Sometime in the future, it will break down. Then the number of cars he's owned will be three; saying 'will have had three cars' suggests that after his third car breaks down, his ownership of these three cars will be complete.