A compound engine assembly for use as an auxiliary power unit for an aircraft and including an engine core with internal combustion engine(s), a compressor having an outlet in fluid communication with an engine core inlet, a bleed conduit in fluid communication with the compressor outlet through a bleed air valve, and a turbine section having an inlet in fluid communication with the engine core outlet and configured to compound power with the engine core. The turbine section may include a first stage turbine having an inlet in fluid communication with the engine core outlet and a second stage turbine having an inlet in fluid communication the first stage turbine outlet. A method of providing compressed air and electrical power to an aircraft is also discussed.