A cubic graph is said to be semisymmetric if its full automorphism group acts transitively on its edge set but not on its vertex set. The semisymmetric cubic graphs of orders $6p$ and $6p^2$ were classified in (Com. in Algebra, 28 (6) (2000) 2685--2715) and (Science in China Ser. A Mathematics, 47 (2004) No.1 1--17), respectively. In this paper we first classify all connected cubic semisymmetric graphs of order $36p$ for each prime p and also classify all connected cubic semisymmetric graphs of order $36p^2$, where $p\neq 5$ and 7 is a prime.