No, the engine oil specifications of API SP and ACEA C3 do not directly meet the specific requirements of VW 502.00 or VW 504.00. While API SP and ACEA C3 are recognized oil standards, Volkswagen (VW) has its own unique oil specifications for their engines.

VW 502.00 and VW 504.00 have specific viscosity and performance requirements that are designed to meet the needs of VW gasoline engines. These specifications ensure compatibility with the engine design and provide the necessary lubrication and protection.

If your vehicle requires oil that meets the VW 502.00 or VW 504.00 specifications, it is recommended to use an oil that explicitly states compliance with those standards. This will ensure that the oil meets the specific requirements set by Volkswagen for optimal engine performance and longevity.

Always refer to your vehicle's owner's manual or consult with an authorized Audi dealership for the correct oil specification and brand recommendations for your 2013 Audi A8 4.0T gasoline engine.