If you're asking if there is a difference between the 2 "increases" being applied when delaying benefits, I don't think there is.
Example: Someone's annual benefit at 62 is $30K/yr but they want to wait until 63 to draw benefits. Let's say at age 63 the COLA is 2% and the 1-year delay creates a 8% bump. Regardless of how to apply the percent increases, you end up with $33,048. It's basically 30K * 1.02 * 1.08 = 33,048. FYI, using these assumptions identically, this becomes $40K and $49K (rounded) at ages 65 and 67.
This is my rough understanding of how it works. Happy to be corrected and I understand that there are other factors that come into play like marriage status, work status, and I imagine the exact month you apply for benefits.
As far as comparing all of these numbers by investing the take-home benefits until you die or hit 100, I don't see the point. Life is meant to be more than numbers on a spreadsheet.
Yep. I doubt that Medicare premium increases are used in calculating CPI and eventually COLA.