Question: In this sentence: 做乜唔叫埋我? What is the function of 埋?

I understood this sentence to be: "why didn't you call me?" (perhaps to an outing or a party). What is the difference with the sentence "做乜唔叫我"?

Insights please.

Answer: 
As verbal suffix, 埋 can function as a verb complement with a lexical meaning somewhat like "close, tight". In this case, it can be used together with an adverb of degree (such as 好，太) and 咗. For example:

1. 唔好企太埋。(Don't stand too close.)
2. 佢关埋咗度门。（He has closed the door (tightly).)

In a sentence like 做乜唔叫埋我?, 埋 functions as an aspect marker. In this case, it cannot be used together with an adverb of degree (such as 好，太) and 咗. And like many other aspect markers in Cantonese (e.g. 住，到，紧，亲...), 埋 "has lost" its lexical meaning through abstraction and become an aspect marker. The interpretation of the process where 埋 is used is a function of it's underlying value and the context.

As an aspect marker, 埋 is used in contexts where we have a class of possible values constructed as fragmentable or dissociable. For example:

3. 唔准玩，做埋啲功课先。(You are not allowed to play. Finish your homework first.)
4. 今日下午我地踢波，叫埋阿民啦。(We are playing soccer this afternoon. Let Ah Min join us.)

In (3), "homework" is constructed as a "fragmentable amount of work". You have already started, but there is still a fragment that remains to be done. In (4), there are a group of people who can play soccer together. 阿民 is singled out in the beginning as the one who may or may not play together.

In these examples, 埋 serves to cancel the fragmentation and return the class as a whole.
做乜唔叫我？ => Why didn't (you) notify me?

做乜唔叫**埋**我？ = 做乜唔預我？ = 做乜唔邀請我？ => Why didn't (you) **also** count me **in**? = Why was I kept out? = Why ain't I **also in**vited?

In English, "**also** count (somebody) **in**" means "**in**vite (somebody) **too**", but "count (somebody)" alone has no such clear meaning.

While both questions sounds accusing, 埋 emphasizes that at lease one person is included in an event yet the asker was kept out.