I just need to know that how to make a data series of real government expenditures using nominal government expenditure data series.
If you have more detailed information about what kind of expenditures you have then you can use the CPI data. Current price data for government does not exist under the price program for BLS for you to use to convert the nominal to reals.
However, you can use the BEA industry data which does have a government sector price indexes for either valued added output, gross output concept of GDP or you can select the government sectors price indexes for intermediate inputs. It depends on the topic you are analyzing.