Find sums of three repeating values

I need to find the sums of sets of three values that repeat every 6, then place these sums onto a new column (M).

For example,
M2 = F3 + F9 + F153
M3 = F21 + F27 + F33
M4 = F41 + F47 + F53


The above is all I currently need, don't feel discouraged of answering because of the long bottom part (I've noticed that longer questions are less likely to be answered). What's below isn't crucial, but if you're willing to help...

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The real challenge is that after row 1400, I added a new line item. Therefore, the pattern becomes 7 then 6.

For example,

M = F1403 + F1410 + F1416.

It would be awesome if you could just help me with the first part, so I could think of a way to tackle the second part. If this helps, I can shed some light on what I am doing (maybe summing by rows is the totally wrong approach):

I have three types of accounts (1,2, and 3), 102 fiscal months, and 8 types of fees associated with a Item Count. I need to sum the monthly cost associated with each type of fee (meaning I need to sum the three accounts per month).
For example, to find the total monthly cost of fee type 2 during July 2003, I need to add up:
Account 1 , Fee Type 2 = 3900
Account 2, Fee Type 2 = 200
Account 3 Fee Type 2 = 100
Which results in 4,200 items in July 2003.