>Is there any way to declare that `A' depends on index `i' and prevent simplification:
No, it's not possible. Both summation and integration ignore declared
dependencies (depends(A,i), for example). The user documentation for
integration mentions this; the documentation for sum doesn't.
A workaround might be to use A(i) instead of A; for example
(%i15) sum(A(i),i,1,n);
(%o15) sum(A(i),i,1,n)
Specialize to A(i) = i^3:
(%i16) %, A(i) := i^3, simpsum,factor;
(%o16) (n^2*(n+1)^2)/4
--Barton