The formulas I described are found in textbooks and used by many financial institutions to illustrate the power of compound interest. They are correct. I think it's simply a misunderstanding as to what you think "compounded monthly" means. Understand that compounding monthly does not mean that the full 6% interest is added to your investment each month. This is a yearly interest rate, not a monthly one. What it does mean is that you get 1/12th of 6% (or .5%) interest per month. What we're really talking about here is a periodic interest rate. It happens that in this case, one period is one month. However, if 6% were compounded quarterly, there would be four periods per year, and 1/4th of 6% (or 1.5%) would be your periodic interest rate. To get the periodic interest rate, take your yearly interest rate and divide it by the number of times your investment is compounded each year.
Let me illustrate with your example. 6% of $10,000 is indeed $600, but since we're compounding this interest monthly (12 times per year), the periodic interest rate is .5% (or .005). We can make an observation and note that the value of your investment at the end of the first year should be no less than $10,600 since this would be the value if the interest were compounded only once. We start with $10,000:
In the end, you'd have a gain of roughly $616.79. This is nothing compared to the $10,000 you thought you'd gained, but it's better than nothing. Think about this: a 6% monthly interest rate would be a 72% yearly interest rate. If you can find a safe investment opportunity that yields a 72% gain, the first thing you should do is let me know!