A challenge for all
0) create two math_counters, the master counter and the end counter.
1) Get the binary numbers that represent the letters.
2) Convert the binary numbers to decimal numbers:
P 01010000 80
R 01010010 82
O 01001111 79
T 01010100 84
O 01001111 79
B 01000010 66
O 01001111 79
R 01010010 82
G 01000111 71
Why did you use all capital letters? I used the capital "P". All the other letters are lower case. So the binary would be:
- P | 01010000 | 80 || p | 01110000 | 112
- R | 01010010 | 82 || r | 01110010 | 114
- O | 01001111 | 79 || o | 01101111 | 111
- T | 01010100 | 84 || t | 01110100 | 116
- O | 01001111 | 79 || o | 01101111 | 111
- B | 01000010 | 66 || b | 01100010 | 98
- O | 01001111 | 79 || o | 01101111 | 111
- R | 01010010 | 82 || r | 01110010 | 114
- G | 01000111 | 71 || g | 01100111 | 103
4) button 1: add 1 to the counter; that's the last number
5) button 2: add 2 to the counter; that's the second last number
6) button 3: add 4 to the counter; that's the third last number
7) button 4: add 8 same for button 5,6,7,8
Just so you know, the rest of the buttons would be 16, 32, 64, and 128; respectively. Thus your buttons would need to output those number.
9) let the master counter compare the logic_compare(s) compare as soon as its value changes. So every time a number changes it's checked against all the logic compares.
10) give the logic compares outputs:
- let the logic_compares kill themselves when they meet the requirement;
- let the logic_compares add 1 to the end counter for the number of correct letters
11) give the math_counter a onhitmax output, you solved the puzzle.
To make it visible for the player you could make a material that has all letters as a texture index; so it is visible for players what is happening 
I could've probably done it somewhat simpler but this works!
I tried to make an animated texture and it refused to display in HAMMMER or in-game. All it showed was the purple checkerboard pattern. I will try again, though.
If you used other number; just change the values in the logic_compares.
I personally would use caps because all the difference it makes is that with lower case letters they all require a cube on 32. 
Seems like that would make it easier. After all, you can insure that the buttons are working by having the 32 button be a sort of test button. Ya know, if the 32 button works the whole thing works or something like that.
I would also like to know if anyone would want to contribute ideas for the various rooms that contain the "letter puzzles". By that I mean if you have any ideas for the rooms that the player has to enter to get the cubes, I would like to hear them. If you allow me to use your idea, I will credit you in-game with an overlay in the appropriate room.
Use PUNT cubes, with a dropper on the floor. The cubes can't come out until you reverse the gravity.
How would I do this?
Oops, I might not have uploaded the instance yet. Anyway, put a dropper on the floor, with a fizzler at the back of it to kill mis-spawned cubes. Then use the PUNT cube instance from the new version of the FGEMOD, which I'm uploading. When you aim at it and click it toggles gravity back and forth (as seen in Reep's upcoming PUNT mod, used with permission).
Do you know what your signature means? It translates to "Emboss are false!"
EDIT: Or more accurately, "We are of falsity EMBOSS!"
"Falsi sumus" is the perfect passive first plural of fallo, fallers, fefelli, falsus ('to deceive'). "Crusto" comes from crustum, crusti ('pastry'). It's a roundabout way of saying "we were deceived by the pastry," in other words, the cake is a lie. It's not very literal, but I couldn't find any sort of word for "a lie." It could also mean "I am embossing is a lie" or any such, due to the unfortunate homophone.
@FelixGriffin: Just out of curiosity, did you upload the newest version of the FGEMod yet? I do like the FGE mod. I just think it could be a little more user friendly.