The common request to present the last process date of Cube XX can be solved by the ASSP project presented at codeplex.

The function in the CubeInfo class is GetCubeLastProcessedDate. This
function will return the date when the current cube was last processed.
The following is an example MDX query against the sample Adventure Works
cube:

with member [Measures].[LastProcessed] as
ASSP.GetCubeLastProcessedDate()
select [Measures].[LastProcessed] on 0
from [Adventure Works]

Download the project and carefully walkthrough the step by step.