Learn Hardcore Icelandic: Allir borða köku.

köku is in the accusative singular.
The direct object of most verbs in Icelandic is in the accusative case.
Since cake here is the object of borða, you need accusative: köku, not kaka.

So:

nominative (subject): kaka
accusative (object): köku

What case is köku, and when do I use that case?

Köku is accusative singular.

You typically use the accusative in Icelandic for:

Direct objects of verbs:
- Ég borða köku. – I eat cake.
- Hún sér hund. – She sees a dog.
After some prepositions that govern the accusative (e.g. um, gegnum, etc.), though that’s a separate topic.

In Allir borða köku, köku is the direct object of borða, so it must be accusative.

Why does kaka change to köku (with ö)?

The change from a to ö is a typical Icelandic vowel change in oblique cases (here, accusative köku).

For the noun kaka (feminine):

nominative: kaka
accusative: köku
dative: köku
genitive: köku

So:

The ending changes (here to -u).
The stem vowel also changes (a → ö) in the non‑nominative forms.

You just have to learn these patterns as part of the noun’s declension. Dictionaries usually show all four singular cases for this reason.

Does Allir borða köku mean “Everyone eats cake” or “Everyone is eating cake”?

It can mean either, depending on context:

Habitual/general: “Everyone eats cake” (they all eat cake in general).
Right now: “Everyone is eating cake” (at this moment).

Icelandic uses the same simple present form (borða) for both English “eat” and “are eating”. Context usually makes it clear which reading is intended.

Why is there no word for “a” or “the” before köku?

Icelandic usually does not use a separate word for the definite article (“the”). Instead it uses a suffix:

For kaka:

“a cake / cake” (indefinite, nominative): kaka
“the cake” (definite, nominative): kakan
“(a) cake” (indefinite, accusative): köku
“the cake” (definite, accusative): kökuna

In Allir borða köku, there is no definite suffix, so köku is indefinite: “cake” / “a cake”.

If you wanted “Everyone eats the cake”, you would say:

Allir borða kökuna.

Why is the verb borða and not borðar or something else?

Borða is the verb “to eat” in the present tense.

Present tense forms are:

ég borða – I eat
þú borðar – you (sg.) eat
hann / hún / það borðar – he / she / it eats
við borðum – we eat
þið borðið – you (pl.) eat
þeir / þær / þau borða – they eat

(In many descriptions you’ll see við borðum, þið borðið, but in casual speech the -um/-ið endings are often reduced; the key point here is 3rd person plural.)

The important bit:

With a plural subject like Allir (“everyone” but grammatically plural), you use the 3rd person plural form: borða.
With a singular subject like hann (he), you’d use borðar:
Hann borðar köku. – He eats cake.

So Allir borða köku is grammatically like “They all eat cake.”

Is Allir grammatically singular or plural? It means “everyone”, which feels singular in English.

Allir is grammatically plural in Icelandic.

Literally, it’s the nominative plural of allur (“all”).
When you say Allir borða köku, it’s as if you said “All [people] eat cake.”
So the verb must agree in the plural: borða, not borðar.

Compare:

Allir borða köku. – Everyone / They all eat cake.
Allur kökuna borðar. – (incorrect) – Verb would be wrong and so is subject form.

Think of Allir more as “all (of them)” than the English grammatical singular “everyone”.

Are there other forms like Allir that I should know?

Yes, allur (“all, every”) has different forms depending on gender and number. In the nominative:

Singular:

masculine: allur
feminine: öll
neuter: allt

Plural:

masculine: allir
feminine: allar
neuter: öll

For people in general (mixed or unspecified group), you typically use allir:

Allir koma. – Everyone is coming.
Allir eru glaðir. – Everyone is happy.

You’d use allar if you refer specifically to a group of women/girls, and öll for a neuter plural noun (or certain abstract/group uses).

Can I change the word order in Allir borða köku?

For a neutral statement, the normal word order is:

Subject – Verb – Object
Allir (subject) borða (verb) köku (object).

You don’t normally say something like *Borða allir köku as a simple statement.

However:

In a yes–no question, you do move the verb to the front:
- Borða allir köku? – Do all (of them) eat cake? / Is everyone eating cake?
In more complex sentences you can put other elements first, but the finite verb still tends to come in second position (the “V2” rule), which is more advanced grammar.

So for now: stick with Allir borða köku for a plain statement.

How would I say “Not everyone eats cake” or “No one eats cake” using this sentence?

Two different ideas:

“Not everyone eats cake.”
Here you’re saying “Some do, some don’t”:
- Ekki allir borða köku. – Literally “Not all eat cake.”
Note the position of ekki:
- Ekki allir borða köku. – Not everyone eats cake.
- Allir borða ekki köku. – Sounds more like Everyone does not eat cake (i.e. no one does).
“No one eats cake.”
Use enginn (“no one”):
- Enginn borðar köku. – No one eats cake.

So:

Allir borða köku. – Everyone eats cake.
Ekki allir borða köku. – Not everyone eats cake.
Enginn borðar köku. – No one eats cake.

How do I pronounce Allir borða köku?

Approximate pronunciation (not strict IPA):

Allir – roughly “at-lir”
- initial A like “a” in father but shorter
- ll is pronounced with a sort of “tl” sound in many dialects
- ir like “ear” but shorter and tenser
borða – roughly “bor-tha”
- o like “o” in bought (British) or bore (American, but shorter)
- ð is a soft “th” as in this (voiced)
- final a like “a” in father (short)
köku – roughly “kœ-ku”
- ö is like German ö in schön, something between e in her and u in burn, but with rounded lips
- final u is a short, relaxed “oo” sound

Said smoothly, Allir borða köku comes out something like:

“AT-lir BOR-tha Kœ-ku” (with Icelandic vowel qualities).