Jeg vil prøve at bage en kage i weekenden.

Vil can cover both ideas, depending on context. In this sentence it most naturally shows intention: the speaker plans or wants to try baking a cake.

So jeg vil prøve... can feel like:

• I will try...
• I want to try...

Danish often uses vil + infinitive to talk about the future, but it is not a separate future tense in the way English learners sometimes expect.

Because vil is a modal verb. In Danish, modal verbs are followed by the bare infinitive:

• jeg vil prøve
• jeg kan bage
• jeg skal gå

So after vil, you do not use at.

Because prøve is not a modal verb. When prøve is followed by another verb, Danish normally uses at + infinitive:

• prøve at bage
• prøve at forstå
• prøve at komme tidligt

So the pattern is:

vil + prøve + at + bage

That is why there is no at after vil, but there is one before bage.

With another verb, prøve at + infinitive means to try to do something.

So:

• prøve at bage = try to bake

If you use prøve without another verb, it usually means try/test/taste something depending on context:

• Jeg vil prøve kagen = I want to try the cake

So prøve and prøve at + verb are related, but they are not used in exactly the same way.

Because kage is a common-gender noun in Danish, so it takes en in the singular indefinite form:

• en kage = a cake

If it were a neuter noun, it would take et, but kage is not one of those.

Its definite form is:

• kagen = the cake

Because kage is a singular countable noun. In Danish, just as in English, you normally need an article with a singular count noun unless there is some other determiner.

So:

• en kage = correct
• bage kage = usually not natural in this sentence

You need the article because the speaker means a cake, not cake in general as a substance.

I weekenden is the normal Danish way to say at/on the weekend when talking about a specific weekend.

Here, i does not literally work exactly like English in. It is just the natural preposition in this expression.

So learners should remember:

• i weekenden = during / on the weekend

Because weekenden is the definite form of weekend:

• en weekend = a weekend
• weekenden = the weekend

In Danish, the expression is idiomatically i weekenden, not usually i weekend.

So even though English says on the weekend, Danish builds it as in the weekend-the, using the noun’s definite ending.

This is a very common question.

• i weekenden usually means this/that weekend, one specific weekend
• om weekenden usually means on weekends, in a habitual or repeated sense

Compare:

• Jeg vil prøve at bage en kage i weekenden.
  = one particular weekend
• Jeg bager tit kage om weekenden.
  = weekends in general

Yes:

I weekenden vil jeg prøve at bage en kage.

That is completely natural.

But when you move something to the front in a Danish main clause, the finite verb still has to stay in second position. This is the famous V2 rule.

So:

• Jeg vil prøve at bage en kage i weekenden.
• I weekenden vil jeg prøve at bage en kage.

Both are correct.

A helpful way to break it down is:

• Jeg = subject
• vil = finite verb / modal
• prøve = infinitive
• at bage = infinitive phrase
• en kage = object
• i weekenden = time expression

So the sentence structure is:

subject + finite verb + infinitive + infinitive phrase + object + time

Yes, but the nuance changes.

• vil often suggests intention, willingness, desire
• skal often suggests plan, arrangement, or something that is supposed to happen

So:

• Jeg vil prøve at bage en kage i weekenden
  = I intend / want to try baking a cake this weekend

• Jeg skal prøve at bage en kage i weekenden
  = I am going to / am supposed to try baking a cake this weekend

Both can work, but they do not feel exactly the same.

Because Danish does not capitalize common nouns the way English does in some contexts. In modern Danish, common nouns are written with a lower-case letter unless they begin the sentence.

So:

• weekend
• kage

are both lower-case. Only proper nouns and the first word of a sentence are capitalized.