Small Business Advanced Cybersecurity Enhancements Act of 2021 This bill requires the Small Business Administration (SBA) to establish a central small business cybersecurity-assistance unit within the SBA and a regional cybersecurity-assistance unit within each small business development center. These units shall serve as the primary means for a small business to communicate cyber threats and defensive measures with the federal government, and the bill prohibits any cause of action against a small business for such communication or for any conduct in response to such communication.