There's a difference between taking a random() and then cubing it, and taking three different random()s and multiplying them together. The EV of the first is 1/4, whereas the EV of the second is 1/8.
You can prove the EVs for yourself, but an intuitive way to think about why the EV of the first is twice as much as the second scenario is to consider their probability density functions. When you cube a single random variable, the resulting PDF is skewed towards lower values, but not as dramatically as when you multiply three separate random variables together.
You can prove the EVs for yourself, but an intuitive way to think about why the EV of the first is twice as much as the second scenario is to consider their probability density functions. When you cube a single random variable, the resulting PDF is skewed towards lower values, but not as dramatically as when you multiply three separate random variables together.