Well-defined AB-type miktoarm star-shaped polymers with a polyhedral oligomeric silsesquioxane (POSS) core are prepared by combination of the core-first and arm-first approaches using ring-opening polymerization (ROP) and copper-catalyzed azide-alkyne cycloaddition (CuAAC) click reactions. The clickable octakis-azido-hydroxyl-POSS as the core molecule and alkyne end-functionalized precursor polymers (methoxypoly(ethylene glycol), poly(methyl methacrylate) (PMMA), and polystyrene) are synthesized independently according to the well-known procedures including ring-opening reaction of octaglycidyldimethylsilyl POSS using sodium azide, etherification of poly(ethylene glycol) (PEG) monomethyl ether using propargyl bromide and sequential atom transfer radical polymerization of methyl methacrylate or styrene and following nucleophilic substitution reactions of the these polymers with sodium azide. In subsequent step, octa-armed poly(epsilon-caprolactone) star-shaped polymer ((PCL)(8)-POSS-(N-3)(8)) containing azido functionalities in the core is synthesized via core-first approach through ROP of epsilon-caprolactone (epsilon-CL). Finally, alkyne end-functionalized polymers are introduced to the (PCL)(8)-POSS-(N-3)(8) via arm-first approach using the CuAAC click reaction under ambient conditions, yielding AB-type miktoarm star-shaped polymers. Based on H-1 NMR spectroscopy calculations, the number of PEG, PMMA, and PSt arms in (PCL)(8)-POSS-(mPEG)(7), (PCL)(8)-POSS-(PMMA)(5), and (PCL)(8)-POSS-(PSt)(6) star-shaped polymers is found as 7.1, 4.9, and 5.9, respectively.