wǒ yígè rén chī bù wán zhè kuài dàngāo, nǐ gēn wǒ yìqǐ chī ba.

我一个人 literally is “I, one person”, but as a set phrase it usually means “I, by myself / alone”.

Pattern:
(pronoun) + 一(个) + 人 → “(pronoun) alone”

• 我一个人 = I alone / by myself
• 你一个人 = you alone
• 他一个人 = he alone

So 我一个人吃不完这块蛋糕 is better understood as
“I can’t finish this piece of cake by myself.”
not “I, one person, can’t finish…”, even though that’s the literal structure.

Yes, you can say:

• 我吃不完这块蛋糕。 – I can’t finish this piece of cake.

Adding 一个人 adds emphasis that you’re on your own:

• 我一个人吃不完这块蛋糕。 – I alone can’t finish this piece of cake.
  (Implying: if someone helps, then maybe we can finish it.)

So:

• Without 一个人: just a statement about capacity.
• With 一个人: highlights the fact that you’d need another person’s help.

吃不完 is a potential complement (a type of resultative complement):

Structure:
Verb + 不 + Result → cannot achieve that result

• 吃 = to eat
• 完 = finished, complete (as a result)
• 吃完 = to finish eating (successfully)
• 吃不完 = cannot finish eating (it’s too much / not possible in general)

So:

• 吃完 focuses on the result actually achieved (finished eating).
• 吃不完 focuses on whether it is possible to achieve that result.

Examples:

• 我吃得完。 – I can finish eating it.
• 我吃不完。 – I can’t finish eating it (capacity, amount).

They’re quite different:

• 吃不完 – cannot finish (in general / by nature or amount).

  • Implies impossibility or lack of capacity.
  • Often used about the future or a general situation.
  • Example: 这么多，我一个人吃不完。
    So much; I alone can’t finish it.

• 没吃完 – did not finish (a fact about what happened).

  • Past or present statement of fact, not about capacity.
  • Example: 我没吃完这块蛋糕。
    I didn’t finish this piece of cake. (Maybe I could have, but I stopped.)

In your sentence, 吃不完 is suitable because you’re predicting you can’t finish it alone.

块 is a common measure word for things that come in blocks, chunks, or pieces, including cake:

• 一块蛋糕 – a piece of cake
• 一块肉 – a piece of meat
• 一块巧克力 – a piece of chocolate

You can say 一个蛋糕, but that means an entire cake (one whole cake), not a slice or piece.

So:

• 这块蛋糕 – this piece of cake (natural here)
• 这个蛋糕 – this (whole) cake (like pointing to a whole cake in a bakery)

If the context is clearly about a slice, people might say 这个蛋糕 in casual speech, but 这块蛋糕 is more precise.

Yes. Common choices:

• 一块蛋糕 – a piece / chunk of cake (very common, neutral)
• 一片蛋糕 – a slice of cake (highlights the thin slice shape)
• 一个蛋糕 – a whole cake

So you could say:

• 我一个人吃不完这片蛋糕。 – I can’t finish this slice of cake by myself.
• 我一个人吃不完这个蛋糕。 – I can’t finish this (whole) cake by myself.

In everyday conversation, 块 is extremely common for cake.

Here, 跟 means “with” (person you are together/doing something with):

• 跟我一起吃 – eat together with me

You can usually replace 跟 with 和 in this sense:

• 你和我一起吃吧。 – You eat together with me.

Differences:

• In spoken Mandarin, 跟 is more common and more colloquial for “with (someone)”.
• 和 is also correct and common; it can feel slightly more neutral or formal in some contexts, but here both sound natural.

So:

• 你跟我一起吃吧。
• 你和我一起吃吧。

Both are fine; 跟 just feels very natural in speech.

一起 means “together”.

Typical patterns:

• 跟/和 + person + 一起 + Verb
  • 你跟我一起吃。 – You eat together with me.
  • 他和朋友一起学习。 – He studies together with his friends.

Position:

• 一起 usually goes right before the main verb:
  • 一起吃, 一起去, 一起玩, etc.

If you move 一起 around too much, it can sound unnatural.
For example, 你一起跟我吃 is not how people normally say it; 你跟我一起吃 is the standard order.

吧 is a sentence-final particle that softens the tone and often turns a statement into a suggestion, invitation, or mild command.

• 你跟我一起吃。 – You eat with me.
  (Can sound like an instruction or decision.)

• 你跟我一起吃吧。 – Why don’t you eat with me / Come and eat with me.
  (Friendly, inviting, less forceful.)

In your sentence, 吧 makes it sound like a warm suggestion:
“Come share this with me.” rather than an order.

Yes, you can say:

• 我一个人吃不完这块蛋糕，你跟我一起吃，好吗？

Differences:

• …吃吧。 – a suggestion / friendly invitation.
  You’re already lightly proposing they do it.

• …吃，好吗？ – seeks confirmation / agreement more explicitly.
  It’s like: “You eat with me, okay? / is that alright?”

Both are polite and natural. 吧 is slightly more compact and “softly pushy”; 好吗？ is more clearly asking for the listener’s opinion or consent.

Both can mean “by myself / on my own”, but with nuance:

• 我一个人 – focuses on number: just one person (me).
  Often used for physical situations: going somewhere, eating, living, etc.

  • 我一个人去。 – I’ll go alone.
  • 我一个人吃不完。 – I alone can’t finish it.

• 我自己 – focuses on self / doing it oneself, often in contrast to someone else doing it.

  • 我自己吃。 – I’ll eat it myself (not giving it to others / not needing help).
  • 让我自己来。 – Let me do it myself.

Sometimes both are possible but with a slight shift:

• 我一个人吃 – I eat alone (nobody else present).
• 我自己吃 – I (will) eat it myself (emphasis on who does the eating).

Yes, 一人 (without 个) is possible and correct:

• 我一人吃不完这块蛋糕。

Nuance:

• 我一个人… is more common in everyday speech.
• 我一人… can sound a bit more concise or slightly literary/formal, though you might still hear it in spoken Chinese.

For a learner, 我一个人… is the safest, most natural-sounding choice in conversation.

Yes, you can say:

• 这块蛋糕我一个人吃不完。

Meaning is basically the same:
“I can’t finish this piece of cake by myself.”

Difference is in focus:

• 我一个人吃不完这块蛋糕。 – starts with “I alone”, focusing on who can’t finish it.
• 这块蛋糕我一个人吃不完。 – starts with “this piece of cake”, making it the topic first, like:
  • “As for this piece of cake, I can’t finish it by myself.”

Both are common and natural. Chinese often puts the topic (what we’re talking about) at the beginning.