will this American Booster work on our cable network.

[bravo_2_zero]

Whether you receive your TV, FM, or HDTV signals over-the-air, through cable, or broadband, this Brand New 36dB signal amplifier with superior specifications will aid you if your signal is weak due to splitting or long in-house cable runs.

Designed for use in medium to large distribution systems amplifying signals
from 30MHz to 850MHz, it works especially well amplifying cable TV and HDTV signals in homes with multiple TVs and/or long cable runs.

Switchable FM trap will eliminate interference from FM broadcasts. Simply adjust the gain control for optimum picture quality. Circuitry designed for maximum stability. Metal housing. Lightening protection. 220-240V AC power. Brand new in retail packaging.

here are the specs

[lincsat]

That should work, just be careful you don't overload the amp - too much signal is as bad as not enough.