What was the name of the Persian capital built by Cyrus the Great?

Pasargadae was the Persian capital built by Cyrus the Great. Founded in the sixth century BC in the homeland of the Achaemenid dynasty, it became Cyrus’s principal royal center and burial place.

The city stood in modern Fars Province, Iran, near the ancient Persian heartland of Anshan. Its palace complexes, audience hall, gardens, and monumental tomb combined Persian, Median, Mesopotamian, and Anatolian influences. The famous formal gardens at Pasargadae are also associated with the early development of the Persian paradise-garden tradition.

Persepolis is the most famous Achaemenid ceremonial capital, but it was founded later by Darius I and developed by his successors. Susa and Ecbatana were also important imperial centers; neither was the capital built by Cyrus. Pasargadae therefore fits both the ruler and the construction period in the question.