I think the answer is 1705.The given summation can be written as

But the second sigma is sum of natural no.s taken two at a time and hence,

.

Substituting this,the summation becomes

Ya..I got the mistake.Since the summation contains 1.2,2.3,3.4.... and also 2.1,3.2,4.3....So,the second sigma which I mentioned is repeated 2 times.Hence the sum is

Now,by substituting the second sigma, gets cancelled and the answer is simply which is [10(10+1)/2]²=[5(11)]²=(55)²=3025.