I looked around for my notes, and I couldnt find much, so I did the calculations again:

I considered 4 circumstances Highest load (240ma), lowest load (20ma), Highest gain guess (100), lowest gain guess (10). Im only using 5v, and saturation point is .7v.

Loads:

1-12 LEDs, assuming 20mA.

20mA to 240 mA

.7v Saturation

Vin=5v

Gain/Beta/HF_E: 10, 100

#1 (20ma load, gain 10)

Base current = 2mA (20/10=2)

5v-.7v = 4.3v

4.3/.002(2ma) = 2150 ohms

Base resistor size 2.15K ohm

#2 (20ma load, gain 100)

Base current 20mA (20/100)= .2

5v-.7v = 4.3v

4.3/.0002 = 21,500

Base resistor = 21.5k ohm

#3 240 mA load, gain 10

Base current = (240/10) =24mA

5v-.7v = 4.3v

4.3/.024 = 179 Ohm

#4 240 mA load, gain 100

Base current = (240/100)=2.4 mA

5v-.7=4.3v

4.3v/.0024 = 1791 ohm

Base resistor =1791 ohms

From there It looks like I have range of 180 to 2k ohms. Which is pretty big, it doesnt help me figure out what part to order, so I cant order parts, until I narrow this down.

To make thing a little more complicated, Im cascading the transistors, so, even if these numbers were 100% accurate, they may not be after the second transistor.

In the past I've done calculations, and later found out that real world numbers and calculations can be very different, its best to test things with the specific parts, and specific power supplies, because they can vary. Sometimes that 5v power supply is only 4.5v, others may be over 5v. 100 ohm resistors may actually be 95 ohms. These seem like tiny insignificant amounts, but when you throw them into the equation, it can change the results quite a bit.

I ended up getting using many resistors and a few transistors, setup a test rig with the parts I plan on using (LEDs, resistors, 2n2222s and a variety of base resistors). I did a bunch of testing and measuring, then I realized that I needed to use 2 transistors for my testing, so that It would be exactly like I will be using them.

I had a lot of hassle trying to measure, since my ranges of measurement was from a fraction of an mA to about 250mA, which meant 2 settings on the meter, and the 2 settings were inconsistent. but my measurements lead me to believe that I could use between 150 and 1k ohm base resistors, 150 drew a lot of current at the base when all LEDs lit (about 40ma), and 1k restricted the current a little bit, 300 ohms seemed to work good, and keep the base current under 20ma. I wasnt able to get 300, but I was able to find 270 ohm resistors, which is what I ended up using.

While I was testing the 2n2222 with 4 RGB LEDs I did similar experiments with the mosfets that I picked out for the other cubes (they need to sink/source almost a amp, way too much for 2n2222s). I have a p-channel, and an n-channel, both have similar ratings, both need to be able to light between 1 and 48 LEDs (assuming 20ma), thats nearly a whole amp. I only did a little measuring, but it seem like they only had about 1ma load on the gate, they seem like a much better part than the BJTs.