To find the sum of the expression 1x2x3 + 2x3x4 + 3x4x5 + ... + 2013x2014x2015, we can use the formula for the sum of an arithmetic series.

The general term of the series is given by tn = n(n+1)(n+2), where n represents the position of the term.

We can rewrite the expression as the sum of the general term from n=1 to n=2013:

S = Σ(n(n+1)(n+2)), where n goes from 1 to 2013.

Using the formula for the sum of an arithmetic series, we have:

S = (2013/2)(1 + 2013)(2013 + 1)(2013 + 2)

Simplifying this expression, we get:

S = (2013/2)(2014)(2014)(2015)

S = 203,604,206,370

Therefore, the sum of the expression 1x2x3 + 2x3x4 + 3x4x5 + ... + 2013x2014x2015 is 203,604,206,370.