What you are looking for is called a spectrum analyzer. A spectrum analyzer is actually a scientific/engineering instrument, but I think you want a spectrum analyzer effect. (You are not trying to make accurate measurements.)
With an LED spectrum analyzer, each column of LEDs represents a frequency band with low frequencies (bass) on the left and high frequencies (treble) on the right.
DISCLAIMER - I've never made a spectrum analyzer.
This is going to be a part of a larger project, and all 4 LEDs in each blue square can be connected to one output pin.
So, that's 6 frequency-bands. There is a nifty 7-band chip called the [u]MSGEQ7[/u] (available from SparkFun). It takes a line-level signal, filters and "measures" the levels in 7 different bands, and multiplexes 7 varying DC voltages into one Arduino input. It requires some special programming to "read" the 7 voltages at the right time and keep them straight, but you can download it and it's a LOT simpler than FFT. and, one chip takes care of all the circuitry on the input-side (two chips if you want stereo).
If you don't want to use all 7 bands, you'll still get good "LED action" out of whatever bands you use.
Sacrificing 18 pins will be hard (one for each 2x2), so if this is possible to do this with any less I'll take that opportunity.
If you don't need dimming and you don't need to control RGB LEDs, The most common solution is a shift register. A shift register takes-in serial data (a sequence of ones & zeros) into one pin (plus a couple of control pins). The output comes-out in parallel with as many bits (or LEDs) as you wish. [u]Here[/u] is some information to get you started. I recommend that you experiment (and learn) about shift registers before you jump-in and try to build the whole project.
I know that most of them usually involve having an audio file set-up before hand.
Usually not... Especially an effect like a spectrum analyzer that's supposed to look like it's controlled by the music. You might find something like that pre-programmed when the show is repeated over-and-over, such as a stage play, a big concert tour, or a show at Disneyland, etc. But most "dance" lighting effects are sound-activated. Most "dance" lighting effects that you buy (such as American DJ or Chauvet) can be either sound activated or DMX controlled. DMX can be programmed, but DMX lights (and stage lighting) are usually operated by a human at the "lighting board", sometimes along with with some programming.
I built an 8-foot tall "Giant VU meter" effect with 24 LEDs in each channel (left & right). (It only works off the volume, nothing is frequency activated.) I used 3 [u]MAX6978[/u] chips cascaded together in each channel. I only needed 4 Arduino outputs and I can individually control/address 48 LEDs. Each channel has it's own data pin, but the clock and latch pins are shared. Since I have a microcontroller and I can address the LEDs individually.... This effect randomly runs in the normal "bar" mode, "dot" mode (one LED on at a time), it runs in reverse (top to bottom), and inverted (LEDs turned-off with sound instead of on), and it does 7 other sequencing effects with many different patterns & options.