Originally Posted by

**schinb64** Write down the numbers 1,2,3,4,... in a row Srike out every third

so

we are left with 1,2,4,5,7,8,10... now write their cumulative sums

of what remains. We are given

1,3,7,12,19,27,37... Now strike out every second

term then add the sums. So we are left with 8,27,64,125,216,...

The pattern is 2^3,3^3,4^3,5^3,...

How can I explain how this happens? I believe I have to write a formula for each step that I do. I do not know if this is right or how I could get the formula. Any help would be very nice. Thank you for your time.