That's an interesting question, what is the cubic volume of a 2d sector? In terms of linear distances of the order of magnitude of charted space there is at least one possible black hole:
Is a subsector 8 parsec x 10 parsec x 1 parsec (80 cubic parsecs) or is it supposed to be spherical such that the two extreme sized of the sphere can be 10 pc apart from each other (5 parsec radius sphere = ~534 parsec^3?
The maximum distance between any two imperial worlds on travellermap is 232.075 parsecs. This is admittedly using euclidean geometry which Traveller does not use, but at least that is an approximate number. Should we presume the imperium is roughly spherical and thus the volume is around 6.5 million cubic parsec? Given local stellar volume then the imperium should contain about 916000 stars.
If we take "empire of 11000 suns" to its literal meaning using the local stellar density of 0.14 stars per cubic parsec that would be a sphere with a radius of 26.57 parsecs. Edge to Edge the imperium would only be 53 or so parsec across.