אני רוצה להביא להם עוגה למסיבה.

Yes. רוצה agrees with the speaker’s gender in the present tense:

• אני רוצה = I want said by a male speaker, pronounced ani rotze
• אני רוצה = I want said by a female speaker, pronounced ani rotza

In normal unpointed Hebrew, both are spelled the same: רוצה.
So the spelling does not show the difference, but the pronunciation does.

Sometimes Hebrew can omit subject pronouns, but here אני is very natural and often helpful.

A key reason is that רוצה in the present tense does not show person clearly by itself. It tells you gender and number, but not necessarily I / you / he / she in isolation. So:

• אני רוצה = I want
• הוא רוצה = he wants
• היא רוצה = she wants

Because of that, keeping אני makes the sentence clear.

להביא is the infinitive, meaning to bring.

After רוצה (want), Hebrew normally uses an infinitive, just like English uses to + verb:

• אני רוצה להביא = I want to bring

So this is a very standard pattern:

• רוצה לאכול = want to eat
• רוצה ללכת = want to go
• רוצה להביא = want to bring

להם means to them or sometimes for them, depending on context.

It is made from the preposition ל־ (to / for) plus the pronoun ending for them.

So:

• להם = to them / for them

This is an indirect object form, not a direct object form.

That means:

• להביא להם עוגה = to bring them a cake / to bring a cake to them

But if you wanted them as the direct object, Hebrew would use something else:

• להביא אותם = to bring them

So להם does not mean plain them by itself.

Because עוגה here is indefinite: it means a cake, not the cake.

Hebrew uses את before a definite direct object, not before an indefinite one.

So:

• להביא להם עוגה = bring them a cake → no את
• להביא להם את העוגה = bring them the cake → את is required

This is one of the most common things English speakers need to get used to in Hebrew.

It can mean different things depending on context.

Most commonly here, למסיבה means something like:

• to the party
• for the party

Hebrew ל־ often covers meanings that English splits into to and for.

Also, in unpointed Hebrew, למסיבה can be ambiguous:

• לְמְסיבה = to a party
• לַמסיבה = to the party

Without vowel marks, both are written למסיבה.
Usually context tells you which one is meant.

Because Hebrew uses ל־ very broadly.

Here the same preposition is doing two different jobs:

• להם = marking the recipient: to them / for them
• למסיבה = marking the destination, purpose, or event: to/for the party

This is normal Hebrew. English often uses different prepositions where Hebrew reuses ל־.

Yes, the word order is very natural.

A common Hebrew order here is:

• subject + want + infinitive + recipient + thing + destination/purpose

So:

• אני רוצה להביא להם עוגה למסיבה

Putting להם before עוגה is very normal when the indirect object is a pronoun like to them.

English does something similar:

• bring them a cake
• bring a cake to them

Hebrew strongly likes להם עוגה here more than moving להם later.

A common pronunciation is:

• ani rotze lehavi lahem uga lamesiba
  if a male speaker says it and למסיבה means to the party

If the speaker is female:

• ani rotza lehavi lahem uga lamesiba

A few stress points:

• להביא = le-ha-VI
• להם = la-HEM
• עוגה = u-GA
• למסיבה = la-me-si-BA or le-me-si-BA, depending on the meaning/vowels

Yes. Hebrew often uses one structure where English has two equally natural options.

So this part can be understood as:

• to bring them a cake
• to bring a cake to them

Both match להביא להם עוגה.

Here is the breakdown:

• אני = I
• רוצה = want
• להביא = to bring
• להם = to them / for them
• עוגה = a cake
• למסיבה = to/for the party, or to a party depending on context

So structurally it is:

• I + want + to bring + to them + a cake + to/for the party

That literal structure helps explain why the sentence is built the way it is.