In this article, we present necessary and sufficient conditions for a graded (trimmed) double Ore extension to be a graded (quasi-commutative) skew PBW extension. Using this fact, we prove that a graded skew PBW extension A=σ(R)〈x1,x2〉 of an Artin–Schelter regular algebra R is Artin–Schelter regular. As a consequence, every graded skew PBW extension A=σ(R)〈x1,x2〉 of a connected skew Calabi–Yau algebra R of dimension d is skew Calabi–Yau of dimension d + 2.