This is the correct one, ケーキを食べたい = I want to eat cake. Best way to learn them (the verbs) is the way you just did it. :D About particles Everything that comes before は is the main topic, ex; 私はケーキを食べたい ( I am the one who wants to eat cake ) and が is the opposite plus other rules... ex; ケーキが好きです Cake is what I like. を is a direct action. like... I play games, I sing songs, I talk etc but you don't always need I, he, she etc... but I assume you already know that. : D You have to think and learn through Japanese way, else it will only confuse you if trying to direct translate from English to Japanese. I hope this helped : D

I forgot を is a particle used when you are performing an action. Ex. I'm eating cookies, I bought a book, etc However, if you want to say you went somewhere (aka performing an action of travel) you have to use the particle に。2. Slight correction to クッキは食べたい。you can say it only if someone asks you about your wanting to eat different options. For ex. Do you want to eat cookies and drink coffee. If you only want cookies you say クッキは食べたいです。 Does this all make sense? Let me know if you have questions :) Also another slight correction. 1. You could use を食べたい structure but it sounds awkward. Obviously we don't want to sound awkward but some Japanese do say it to not sound eager about wanting something.

Okay I asked my Japanese friend about the difference. 1. Cookie in katakana is クッキ。2. The ending たい implies a desire/want to do something. 3. So クッキが食べたい means I want to eat cookies. 5. You can't say クッキは食べたい or クッキを食べたい。it's not grammatically correct. The particle は pronounced wa when it's used in this structure, is a topic marker. が is a particle that puts extra emphasis on something. There are sentence structures where you HAVE to use it. 6. Sometimes は and が can replace each other in sentences but it depends on the sentence and where you want to place the emphasis. 7. If you want to ask someone "Do you want to eat cookies?" You say クッキが食べたいですか？If you want so ask someone "do you eat cookies?" You say クッキをたべますか? 8. ますis polite ending for verbs. 9. Vervs have different endings based on politeness level and what you want to say/ask. Hope that answers your first question. I'm still learning kanji. Let me know if you need a study buddy :D

Heh, the formatting completely messed itself up since this was apparently a "comment", not an "answer". Oh well, I posted the same thing in my notebook as well if you want to read it there: http://www.italki.com/entry/538874

I just want to add a bit to the other answers, because I feel they are not really correct. The thing is, all three of those sentences are actually grammatically correct. Depending on what you want to say, you can use different particles to put an emphasis on different things. Assuming you meant all three as sentences, not questions, here's what they mean: ケーキを食べたい。 This one is the simplest one. I want to eat cake. Doesn't imply anything else, you just happen to want to eat cake. ケーキが食べたい。 You put emphasis on the cake here. I want to eat *cake* (as opposed to something else). This is the most common way of using this sentence structure. ケーキは食べたい。 Admittedly, only saying this without the proper context might be a bit incorrect, but it does have some uses. For example, when comparing two (or more) options against each other; ケーキは食べたいけど、アイスクリームは食べたくない。 Like Delisha mentioned, you could say only ケーキは食べたい if it's a reply to someone asking a question, but what you basically do then is actually leave the "～たくない" part unsaid, because it's insinuated that you don't want the other option(s) (kind of how you drop 私) . I hope this cleared things up and that I didn't make it too complicated. I tried to keep it simple, but the last example with は is kind of hard to explain.