Do you have a datasheet on the LED module?
You may need a transistor, or a transistor array (8 drivers in one package, such as ULN2803, look it up www.ti.com
) may suit your needs.
Depending on the current flow needed, a shift register such as TPIC6B595 may suit your needs, also combining shift register, high current drive that can handle 12V, and with an output enable line to also support dimming (of all 8 outputs) via PWM.
Depending on your modules, you may be able to drive 2 modules with 1 shift register output, so you would need 7 shift registers (8 bits each, for 56 total).
Any Arduino would be sufficient as you really just need 4 control lines (serial_data_out, serial_shift_clock, data_output_latch, and PWM).