Here is the formula which I arrived at after analyzing Drake's Turn 150 Game:
((2.5*900) * 2.4) * 1.3 = 7020
Multiple 51 Monolith III's by 7020 = 358020 which the game rounds up to show 359K, 359K, 359K for many of Drake's RingWorlds with 51 Monolith III's plus a Robotoid Factory.
This represents 2.5 for the 250% minerals.
The 2.4 is 100% bonus for population + 20% to each resource from his racial points + 20% happiness bonus. The final 1.3 is the Robotoid Factory.
The big thing that threw me for so long was the 5% Worker cultural trait. The consensus right now is that this is never added in. For the final score, multiple everything by 1.3 to show the effect of the System Robotoid Factory III.
Another example is a medium world with 18 facilities:
((2.5*900) * 1.7) * 1.3 = 4972
17 * 4972 = 84532 which the game shows as 85KT for each resource.
The only difference here is the 30% population bonus instead of 100%. Thus, we have 1.7 instead of 2.4.
Hope this helps. By my calculations applied to a couple other of Drake's planets plus some new games I started, the math seems to hold. Let me know if anyone has other ideas.