2 added 65 characters in body

This isn't the answer you seek, but let me observe merely that if you allow extra balls and if the table width is an integer number of balls in each direction, then we may imagine a cross pattern with the cue ball at the intersection.

/------------------\
|         O        |
|         O        |
|         O        |
|         O        |
|OOOOOOOOOCOOOOOOOO|
|         O        |
(         O        )
|         O        |
|         O        |
|         O        |
|         O        |
|         O        |
\------------------/


Under your idealized physical interactions, it seems that the cue ball cannot move, since the forces acting on the other balls are all transverse.

Probably one can also imagine other highly-packed arrangements.

1

This isn't the answer you seek, but let me observe merely that if you allow extra balls and if the table width is an integer number of balls in each direction, then we may imagine a cross pattern with the cue ball at the intersection.

/------------------\
|         O        |
|         O        |
|         O        |
|         O        |
|OOOOOOOOOCOOOOOOOO|
|         O        |
(         O        )
|         O        |
|         O        |
|         O        |
|         O        |
|         O        |
\------------------/


Under your idealized physical interactions, it seems that the cue ball cannot move.

Probably one can also imagine other highly-packed arrangements.