Question:
Which permission controls cube publish in Strategy 9.4.1?
Answer:
The Read permission under cube Properties->Security controls cube publish.

The right-mouse-click menu is as below if the user has full control to the cube.
Strategy Web:

Strategy Developer:

The right-mouse-click menu is as below if the user has all the other permissions expect Read. The user can create and run reports\documents based on the cube, but the user cannot publish the cube in Strategy Web, Developer and Office.
Strategy Web:

Strategy Developer:
