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In DAX, the general measure pattern is as follows
Inventory :=
CALCULATE (SUM ( Inventory[StockCount] ),
LASTNONBLANK (Calendar[Date],CALCULATE ( SUM ( Inventory[StockCount] ) )))
this is pattern will work regardless of there being a count for every date (it will find the last count).
It will be possible but you will need to add a calculated measure to your cube. Are you using Tabular or Multidimensional? Both will work but one will use DAX while the other will need an MDX formula.