Is it possible to calculate the total resistance of this circuit with series and parallel analysis?
If by "parallel and series analysis" you mean combining resistors in series and parallel until you have a single resistor then no, you can't use that kind of analysis because there aren't any resistors in series or parallel to combine. I would be inclined to use node voltage analysis myself.

However, other people might prefer other methods of analysis, such as source transformation or delta-wye transformation. I usually just go for a nodal analysis because it is a general technique and I know it will work.