Final answer:
The fallacy shown in the example blaming atheism for the bloodshed of Hitler's and Stalin's regimes is a False Cause fallacy. This is due to the assumption that atheism caused these historical events without sufficient proof, ignoring other factors.
Step-by-step explanation:
The fallacy in the statement 'The 20th Century is the bloodiest in the history of the world. It's no coincidence that much of the bloodshed was due to two atheistic and godless regimes: Hitler's and Stalin's. This is overwhelming evidence that atheism is false.' is a False Cause fallacy. This fallacy occurs when it is assumed that because one event follows another, the first event must be the cause of the second. The logic is faulty because it assumes without sufficient proof that atheism led to the bloodshed caused by Hitler's and Stalin's regimes, ignoring other complex historical, political, and social factors.
Two other common fallacies one might encounter are Hasty Generalization, where a conclusion is drawn with insufficient evidence, and Ad Hominem, which involves attacking the person making an argument rather than the argument itself. However, in the given statement, the connection made between atheism and the acts of two regimes in terms of causation is a clear example of a False Cause fallacy.