The "analysis" of this issue the government will give you is so simplistic as to be useless, and unfortunately the government line is repeated by many large financial advisors.
Calculation of a "break-even" age must consider the return on investment you receive on your other retirement savings. I did this calculation as I approached 62, several years ago. From memory, If I have savings which I can draw from and my options are SS at 62 vs. drawing the same amount from savings each year until I am 66, the break-even age is late 80s if the return on my savings is 7%, and I will never break even if I can get 8% on my own money.
Since stock market returns average 10-11% in simple index funds, the only reason to delay taking SS even a minute beyond age 62 is if one has very little savings and intends to work until 66.
I took SS at age 62, and have been very pleased with the result. I kept my money in my investments, which I control. If you have a financial advisor, and he suggests anything else, fire him and get someone who understands the time value of money. Similarly, if your financial advisor has your savings allocated to a lot of fixed income investments, your later years will be lean and sparse. Ask him if he understands the concept of "phantom bonds". Essentially the idea that SS and a pension represents streams of income which should be treated as the return on a fixed income investment. This tilts your asset allocation to more equities. If he does not understand this find someone who does.
I took SS at age 62, and have been very pleased with the result. I kept my money in my investments, ....I worked the figures (because I didn’t have anything else to ) and found that over the years with the year end statement I got from SS, I would have $950,00, or more, amoritized to more than 3X, what I have from this scam. I only want my investment back. I’m gonna die before I get it back. If I could invest in the S&P over the last 59 years, my family could be rich.