Sure, just add the same calculation to the GROUP BY
clause:
select dateadd(day, -7, Convert(DateTime, mwspp.DateDue) + (7 - datepart(weekday, mwspp.DateDue))),
sum(mwspp.QtyRequired)
from manufacturingweekshortagepartpurchasing mwspp
where mwspp.buildScheduleSimID = 10109 and mwspp.partID = 8366
group by dateadd(day, -7, Convert(DateTime, mwspp.DateDue) + (7 - datepart(weekday, mwspp.DateDue)))
order by dateadd(day, -7, Convert(DateTime, mwspp.DateDue) + (7 - datepart(weekday, mwspp.DateDue)))
Edit after comment:
Like all questions regarding the optimiser, the answer is really "it depends", but most likely it will only be performed once - you'll see this in the execution plan as a Compute Scalar operator.
Based on this Compute Scalar operation, the optimiser will then decide how to perform the actual aggregation.
The other answers here (CTE/subquery, etc) are all equally valid, but don't really change the logic - ultimately they will be performing similar operations. SQL Server might treat them differently but it's unlikely. However they will help with readability.
If you're worried about efficiency you can look at a couple of options, e.g. setting up the calculation as a persisted computed column and using this in an index, or adding interim results into a temporary table.
The only way to really know for sure is to inspect the Execution Plan/IO statistics when running the query on a typical data set and seeing if you're satisfied with the performance; if not, perhaps investigating one of the above options.