CTERA Networks said Monday it would be an important subcontractor in a major U.S. government contract to help it build a private cloud network that will enable different parts of America’s sprawling defense establishment to share classified and unclassified files and work together online. The company said its technology would be integrated into the framework of a $427 million project to upgrade the data storage system being led by St. Louis-based World Wide Technology for the Defense Information Systems Agency, which supplies computerization and information security for various federal agencies, among them the Defense Department, the U.S. Army and the White House.