Yes! Sparta notably founded only a single colony, the city of Taras on the heel of Italy, which is now the major port city of Taranto. There are various stories explaining how and why the city was founded. Most point to a group of individuals known as the partheniae, who were free, albeit low-ranking, residents of Sparta. Unlike the more famous spartiates, Spartan citizens who completed their training in the agoge and remained in good standing in their barracks, the partheniae were likely descendants of perioikoi, "dwellers-around," Lacedemonians who were neither Spartan citizens nor helots, enslaved serfs. Either forced from their homes because they lacked full citizenship, or voluntarily relocating to find better opportunities, the partheniae settled Taras in the late 8th century BC. Herodotus mentions an early king of the city, Aristophilides, so it is possible that the city modeled its initial government on its mother city. But no evidence suggests that it had any sort of military training system on a scale similar to Sparta. It was at best a middling power in Magna Grecia, the Greek cities in Italy, often vying with the other Greek cities of Italy, such as Region, or the native populations of Samnites, Iapygians, or Messapians for control of local territories. It did maintain at least some connection to Sparta, evidenced by its support of Sparta in the Peloponnesian War (Thucydides tells how the Tarantans denied Athens anchorage in the city and sent a fleet to aid Sparta in the wake of the Athenian disaster in Sicily).

Check out some documents that Tufts University makes available for more primary source reading.