Learn Hardcore Icelandic: Við bökum köku saman á sunnudögum.

Við – we (subject pronoun, nominative case)
bökum – bake (present tense, we form of the verb baka)
köku – cake (accusative singular of kaka, the direct object)
saman – together
á – on (preposition)
sunnudögum – Sundays (dative plural of sunnudagur, used here for a habitual time expression)

So the whole sentence means roughly: We bake cake together on Sundays.
(In natural English: We bake a cake together on Sundays.)

Why is it bökum and not baka or bakar?

Baka is the dictionary form (infinitive: to bake).

In the present tense, baka is conjugated like this:

ég baka – I bake
þú bakar – you (singular) bake
hann/hún/það bakar – he/she/it bakes
við bökum – we bake
þið bakið – you (plural) bake
þeir/þær/þau baka – they bake

So with við (we), the correct form is bökum.
The change a → ö is a regular vowel change called u‑umlaut that happens in some verb forms when a u follows in the ending (here: -um).

Why is it köku and not kaka or kökur or kökuna?

The base word is kaka (cake). Icelandic nouns change form for case, number, and definiteness.

Relevant forms of kaka:

kaka – nominative singular (subject form, a cake)
köku – accusative singular (object form, a cake)
kökur – nominative plural (cakes)
kökuna – accusative singular, definite (the cake)

In the sentence, cake is the direct object of bökum, so it must be in the accusative singular: köku.

There is no definite meaning (the cake) here, so we do not use the definite form kökuna.

Why is there no word for a before köku? Why isn’t it *a köku?

Icelandic has no indefinite article (no word for a/an).

kaka / köku can mean a cake or just cake, depending on context.
The definite article (the) is usually a suffix attached to the noun (for example kakan = the cake in nominative, kökuna = the cake in accusative).

So köku by itself naturally corresponds to English a cake (or just cake) in this context. You never add a separate a in Icelandic.

Why do we use á sunnudögum and not á sunnudag or á sunnudegi?

Icelandic uses different cases to express time. With days of the week:

á sunnudag (accusative singular) – on Sunday (a specific/one Sunday)
á sunnudegi (dative singular) – often on Sunday (as a point in time), depending on context
á sunnudögum (dative plural) – on Sundays (habitually, every Sunday)

Here we are talking about a repeated, habitual action, so dative plural is used: á sunnudögum – on Sundays (in general).

Why does á take the dative in á sunnudögum? I thought á could take accusative.

The preposition á can govern either accusative or dative, and the choice affects the meaning:

á + accusative – often direction or movement onto something, or a specific limited time
á + dative – often location on something, or time as a general setting / recurring time

For recurring days like on Sundays, you use á + dative plural:

á sunnudögum – on Sundays (habitually)

So here á takes dative because we are talking about a regular time frame, not movement.

What exactly does saman mean, and where can it go in the sentence?

Saman means together and is an adverb.

In Við bökum köku saman á sunnudögum, it modifies bökum and tells us that we bake together.

Possible placements (all acceptable, with slightly different emphasis):

Við bökum köku saman á sunnudögum. (neutral)
Við bökum saman köku á sunnudögum. (slight emphasis on doing the baking together)
Við bökum köku á sunnudögum saman. (together, and this happens on Sundays – sounds a bit more afterthought‑like)

Putting saman right after the verb or the object is most natural. You normally would not put saman at the very beginning of the sentence in this case.

Could this sentence also mean We are baking a cake together on Sundays, or only We bake a cake…?

Icelandic does not have a separate progressive form (am/is/are baking) like English.

The present tense bökum can mean both:

We bake a cake together on Sundays (habitual)
We are baking a cake together on Sundays (also habitual in English, though less common)

In context, because of á sunnudögum (on Sundays in general), the sentence clearly describes a habitual action, not something happening right now this moment.

Do we really need the pronoun Við? Doesn’t bökum already show that it is we?

The verb ending -um in bökum does indicate 1st person plural (we), so grammatically you could drop við and say only Bökum köku saman á sunnudögum.

However:

In normal, neutral Icelandic, the subject pronoun (við) is usually kept.
Dropping við can sound more like a command (Let’s bake a cake together on Sundays) or a stylistic shortcut.

So in standard, neutral speech for a statement, Við bökum köku saman á sunnudögum is the natural form.

How do you pronounce Við bökum köku saman á sunnudögum?

Approximate pronunciation (for an English speaker):

Við – like vith, with the ð as the soft th in this.
bökum – BÖH‑kum.
- ö is like the u in burn (British) or like German ö.
- u in -um is short, like oo in book but shorter.
köku – KÖH‑ku (same ö as above; final u is short).
saman – SAH‑man, stress on the first syllable, a like in father.
á – like ow in cow, but shorter and more closed.
sunnudögum – roughly SU-nu-thœy-gum:
- su – su as in soon but shorter.
- nnu – short nu.
- dö – dœ, same ö sound.
- g before u here is a hard g sound.
- final um like in bökum.

Stress in Icelandic is almost always on the first syllable of each word: VIð BÖ‑kum KÖ‑ku SA‑man Á SUN‑nu‑dö‑gum.