Wave-particle　complementarity　lies　at　the　heart　of　quantum　mechanics.　To　illustrate　this　mysterious　feature,　Wheeler　proposed　the　delayed-choice　experiment,　where　a　quantum　system　manifests　the　wave-or　particle-like　attribute,　depending　on　the　experimental　arrangement,　which　is　made　after　the　system　has　entered　the　interferometer.　In　recent　quantum　delayed-choice　experiments,　these　two　complementary　behaviors　were　simultaneously　observed　with　a　quantum　interferometer　in　a　superposition　of　being　closed　and　open.　We　suggest　and　implement　a　conceptually　different　quantum　delayed-choice　experiment　by　introducing　a　which-path　detector　(WPD)　that　can　simultaneously　record　and　neglect　the　system＇s　path　information,　but　where　the　interferometer　itself　is　classical.　Our　experiment　is　realized　with　a　superconducting　circuit,　where　a　cavity　acts　as　the　WPD　for　an　interfering　qubit.　Using　this　setup,　we　implement　the　first　twofold　delayed-choice　experiment,　which　demonstrates　that　the　system＇s　behavior　depends　not　only　on　the　measuring　device＇s　configuration　that　can　be　chosen　even　after　the　system　has　been　detected　but　also　on　whether　we　a　posteriori　erase　or　mark　the　which-path　information,　the　latter　of　which　cannot　be　revealed　by　previous　quantum　delayed-choice　experiments.　Our　results　represent　the　first　demonstration　of　both　counterintuitive　features　with　the　same　experimental　setup,　significantly　extending　the　concept　of　quantum　delayed-choice　experiment.