Federal Cybersecurity Workforce Expansion Act This bill establishes two pilot programs to train individuals in cybersecurity: an apprenticeship program and a program for veterans and military spouses. First, the bill establishes an apprenticeship pilot program to train and prepare up to 25 participants per year for information technology, cybersecurity, or other cyber-related functions within the Department of Homeland Security (DHS). The bill authorizes DHS to implement the program via contracts with or grants to certain eligible entities (e.g., an education and training provider). Participants must agree to remain employed in a federal cyber workforce position for a specified period of time after the completion of the program. Next, the bill establishes a pilot program to provide cybersecurity training to veterans and military spouses. The program must include coursework and training that, if applicable, qualifies for postsecondary credit toward an associate or baccalaureate degree at an institution of higher education; virtual learning opportunities; hands-on learning and performance-based assessments; federal work-based learning opportunities and programs; and the provision of recognized postsecondary credentials to eligible individuals who complete the pilot program. When implementing the program for veterans and military spouses, DHS must coordinate with relevant agencies to (1) leverage existing education and training resources, (2) ensure that participants can use educational assistance while participating in the program, and (3) identify interagency opportunities that enable participants to acquire the competencies and capabilities necessary for federal employment. Each pilot program is authorized to last for five years.