It is pretty obvious that $DTime(n^3) \subseteq PSpace$, since $DTime(n^3) \subseteq DSpace(n^3) \subseteq PSpace$, but I fail to see how to find such a language $L$ so that $L\in PSpace\,\,\,$  yet $\,\,L\notin DTime(n^3) $. Can someone assist with an idea of how to find such $L$?
Proving $DTime(n^3) \subset PSpace$
complexity theory
Hint: Use the time hierarchy theorem which shows, for example, that $\mathsf{DTIME}(n^3) \subsetneq \mathsf{DTIME}(n^4)$.