Problem 42935. Sums of cubes and squares of sums

I did not originally look to see exactly how far one could go. It looks like, IF one is careful in the important expression, you should be able to get to 3329020. I'd expect that the code I'd write that would solve this to go as far as 3329020 would employ an initial test to know if n is even or odd, changing the expression I'd write depending on the parity of n. Of course that branch would also increase the complexity, so raising the Cody score.

Can someone point me in the right direction?
n = 1e5;
y_correct = uint64(500010000050000);
I get 500010000050005. I do not know how to go beyond double precision.

function y = cubesLessSquare(n)
% Formula
N = (((sum((1:n).^3)*2 - sum(1:n)^2)*2/n))
% double to char
C = sprintf('%f',N)
% char to vector
Y = C - '0'
% take out the dot and the numbers after the dot
Dot = find(Y<0)
Y([Dot:end]) = []
% join the the numbers
Z = sprintf('%d',Y)
% make to double
y = str2num(Z)
end

I was trying to be clever by subtracting off sum(a) to keep sum(a^3) low. Imagine my disappointment when this turned out to be an algebra problem!