Technically, you answered your own question. Something immortal cannot die. In Greek mythology the only immortal being ever "killed" were two of the "lesser" Titans (that is, they were children of the 12 ruling Titans).
I would add that no immortal creature has ever been observed under laboratory conditions so the only possible answer is 'we don't know'.
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Eight Immortals - film - was created in 1971.
Apollo is the God that Zeus kills in Immortals.
A Son of the Immortals - 1916 was released on: USA: 22 May 1916
The Greek gods were immortal - they could not die.
At the moment there is no set plans for making a 2nd one. That does not mean its out of the question as the movie did well in the box office and in selling dvd/blue ray. So if made good profit so there is a chance. They did end it in a way that there may be a war of the gods and immortals so just keep eye out for any information.