by Poisonguy
Also not all 3 of the eradicated diseases were cured. Only the yellow one was cured.
You can remove all the cubes of one color before you cure them, but that disease is not considered eradicated. First, you have to gather five cards of that color and turn them in at a research station. Then the disease is considered cured. If there are no cubes of that color on the board at the time of curing, the disease is considered eradicated. If there are cubes of that color, you have to remove them all before eradicating the disease.
It appears at the time that you faced the second Epidemic, you only had one cured disease and none were eradicated. During each turn, you should have been placing down 2 cubes of the color of the card drawn from the infection deck. Meaning each round in a 4 player game you would be placing 8 cubes on the board (in addition to the 18 already there).
Finally, in order to eradicate 4 diseases so quickly, each player would have to start the game with 2 cards of the same color, but each player would get cards of separate colors (player 1: 2 blue cards; player 2: 2 yellow cards; player 3: 2 black cards; player 4: 2 read cards). And after each turn, each player would have to draw two cards of the same color and matching the color of the cards they already have. And this would have to go on into the second turn where they'd all have to draw a 5th card of the same color of their other 4 cards. And been able to both keep every cube from the infect step off the board AND returned to a research station to cure diseases. In the meantime, at least 34 cubes have been placed on the board since the beginning of the game (18+8+8).
NOTE: it doesn't have to go as described above, but it has to be pretty close to it; all the stars have to align.
I can't see how one would eradicate 3 diseases and cure a 4th in that time.
Since you considered the removal of the initial cubes an eradication of the diseases, which they were not, you made a huge mistake. First you cure, then you eradicate. I suggest you reread the rules and start over.