\(A=5^2+10^2+15^2+...+2015^2\\ \Rightarrow A=5^2\left(1^2+2^2+3^2+...+403^2\right)\)
\(B=1^2+...+403^3\\ =1\left(2-1\right)+2\left(3-1\right)+...+403\left(404-1\right)\\ =1.2-1+2.3-2+...+403.404-403\\ =\left(1.2+2.3+3.4+...+403.404\right)-\left(1+2+...+403\right)\)
\(C=1.2+2.3+3.4+...+403.404\\ \Rightarrow3.C=1.2.3+2.3.\left(4-1\right)+3.4\left(5-2\right)+...+403.404\left(405-402\right)\\ =1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+403.404.405-402.403.404\\ =403.404.405\\ \Rightarrow3.C=65938860\\ \Rightarrow C=21979260\)
\(D=1+2+...+403\\ =\dfrac{\left(403+1\right).403}{2}=81406\)
\(\Rightarrow A=25.B=25.\left(C-D\right)=25.\left(21979260-81406\right)\\ =25.21897854=547446350\)
\(\left(1^2-2^2\right)+\left(3^2-4^2\right)+...+\left(2015^2-2016^2\right)\\ =\left(1-2\right)\left(1+2\right)+\left(3-4\right)\left(3+4\right)+...+\left(2015-2016\right)\left(2015+2016\right)\\ =-1-2-3-4-....-2015-2016\\ =-\left(1+..+2016\right)\\ =-\dfrac{\left(2016+1\right).2016}{2}=--2033136\)
