syracuse was a colony of Corinth
it became involved with sparta in the second part of the Peloponnesian war, the "Sicilian expedition". where athens tried to take Syracuse and all of sicily to boost up its trade empire, and get more money to defeat the spartans.

Gylippus of Sparta came to the island trained the natives in the way of the spartans and kicked the athenians out.

that's the relationship of Sparta and Syracuse in a nutshell.