<s>[INST] Sum of series:$ 1+(1+2+4)+(4+6+9)+(9+12+16)+.....+(361+380+400)$ How to find the sum of series 
$$ 1+(1+2+4)+(4+6+9)+(9+12+16)+.....+(361+380+400)$$
I have the problem in finding the nth term of the series. Please suggest me the procedure.
 [/INST] Your terms look something of the form:
$$a_0 = 1, a_1 = (1+2+4) = 1^2 + 1\cdot 2 + 2^2$$
$$a_2 = (4 + 6 + 9) = 2^2 + 2\cdot 3 + 3^2$$
$$a_{19} = (19^2 + 19\cdot 20 + 20^2)$$
$$\sum_{j=0}\big[j^2 + j(j+1) + (j+1)^2\big]$$
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