sono keeki ha mou sinagire nandesu.

その means that and refers to something near the listener or something already mentioned in the conversation.

So その ケーキ means that cake.

This is part of the こ・そ・あ・ど series:

• この = this
• その = that
• あの = that over there

In this sentence, the speaker is talking about a specific cake the listener can identify.

The particle は marks ケーキ as the topic of the sentence.

So the sentence is structured like:

• As for that cake, it is already sold out.

Using は gives a sense of regarding that cake...

If you used が, it would sound more like you are identifying the cake itself as the thing that is sold out, rather than setting it up as the topic. In many situations, は is the natural choice here because the cake is already known in the conversation.

もう here means already.

So もう 品切れ means already sold out.

It often shows that something has happened sooner than expected or that the state is now complete.

Examples:

• もう いいです = It’s fine now / No more is needed.
• もう 食べました = I already ate.

In this sentence, it tells you the cake is not just sold out, but that it has already happened.

品切れ means sold out, out of stock, or no longer available.

It is a noun, but in Japanese nouns can often function like predicates when followed by です or なんです.

So:

• 品切れです = It is sold out.
• 品切れなんです = It is sold out, you see / the thing is, it’s sold out.

You will often see 品切れ in shops, restaurants, and online stores.

Because もう is an adverb, and adverbs often directly modify what comes after them without a particle.

So:

• もう 品切れ = already sold out

This is normal Japanese word order. No particle is needed.

Japanese does not always need a separate verb like English is in the same way.

Here, 品切れ is a noun-like word, and なんです works as the explanatory copula at the end.

So the sentence effectively means:

• That cake is already sold out.

The is idea is carried by です / なんです, not by a separate verb like in English.

なんです adds an explanatory or background-giving tone.

It often feels like:

• you see
• the thing is
• actually
• it’s that...

So 品切れなんです is softer and more explanatory than just 品切れです.

It can be used when:

• giving a reason
• explaining a situation
• responding politely
• adding context the listener may need

For example, in a bakery, if a customer asks for a cake, saying その ケーキ は もう 品切れ なんです sounds like a polite explanation: That cake is already sold out, you see.

Both are possible, but they feel slightly different.

• 品切れです = It is sold out.
• 品切れなんです = It is sold out, you see / the thing is, it’s sold out.

なんです sounds more explanatory and often softer in customer-service situations.

It can also imply:

• this is the situation
• this is the reason
• I’m letting you know the background

So in a shop, なんです can sound more natural and polite than a plain statement.

This happens because 品切れ is a noun.

When んです follows a noun or a na-adjective, you usually need な before it:

• 学生なんです
• 静かなんです
• 品切れなんです

But with an i-adjective or a verb, you do not add な:

• 高いんです
• 行くんです

So the な is there because 品切れ behaves like a noun here.

It is basically a noun, but it can behave in a predicate-like way when used with です.

That is very common in Japanese. Many words that are translated like English adjectives are actually nouns or na-adjectives in Japanese structures.

So although in English we say sold out like an adjective, in Japanese 品切れ is treated grammatically more like a noun expression:

• 品切れです
• 品切れなんです

Yes. That is completely natural.

The difference is mainly tone:

• そのケーキはもう品切れです = a straightforward polite statement
• そのケーキはもう品切れなんです = a more explanatory or context-giving statement

If a customer asked for that cake, なんです may sound a little more considerate because it feels like you are explaining the situation rather than just stating a fact.

It sounds like a polite explanation, often in response to a question or request.

For example:

Customer: That cake, please.
Staff: その ケーキ は もう 品切れ なんです。

The nuance is not just It’s sold out, but more like:

• I’m sorry, that cake is already sold out.
• The thing is, that cake is already sold out.

So the sentence has a gentle, informative tone.

Yes. In normal Japanese writing, it would usually be written without spaces:

そのケーキはもう品切れなんです。

Spaces are often added only in beginner materials to make reading easier.

ケーキ is a loanword, borrowed from English cake.

It is written in katakana, which is commonly used for:

• foreign loanwords
• onomatopoeia
• emphasis
• some names

So ケーキ is the standard Japanese word for cake.