After contacting grafana directly I received the answer that this is not currently possible. All such computation must be done by the data source, not by grafana.

I am guessing that you cannot combine two statements in one query. Try setting the variable in a subquery:

SELECT UNIX_TIMESTAMP(Datum) as time_sec, Datum, Sachkosten as value,
       'Sachkosten' as metric,
       (@csum := @csum + Sachkosten) as cumulative_sum
FROM aufwand CROSS JOIN
     (SELECT @csum := 0) params
ORDER BY Datum ASC;

Or, perhaps this will work:

SELECT UNIX_TIMESTAMP(Datum) as time_sec, Datum, Sachkosten as value,
       'Sachkosten' as metric,
       SUM(Sachkosten) OVER (ORDER BY Datum) as cumulative_sum
FROM aufwand CROSS JOIN
     (SELECT @csum := 0) params
ORDER BY Datum ASC;

Note that in newer versions of MySQL, the ORDER BY may not affect the ordering of the cumulative sum. You would need a subquery with the ORDER BY to ensure that.