The correct word to fill in the blank is "some." The sentence should read: "I've bought some cakes to give away. Would you like one?"

**Explanation:**

1. **Context of the Sentence:** The sentence indicates that the speaker has purchased multiple cakes with the intention of giving them away. The word "some" is appropriate here because it refers to an unspecified quantity of cakes, which fits the context of the sentence.

2. **Grammar and Usage:**
- "Some" is used when referring to an unspecified amount of something that is more than one but not specified.
- The sentence structure implies that the speaker has more than one cake, and "some" is a common word used in English to indicate an indefinite quantity.

3. **Alternative Words:**
- Words like "many" or "several" could also fit grammatically, but they change the nuance of the sentence. "Many" implies a large number, and "several" implies more than a few but not a large number. "Some" is more neutral and commonly used in everyday conversation.

Therefore, "some" is the most suitable word to complete the sentence naturally and accurately.