I don't quite understand your point about not using the function sum. But it is definitely possible to not use any form of loop.
suppose A is a matrix. sum(A) or sum(A, 1) calculates the sum along the first dimension (row). It gives the sum of each column, thus resulting you a row vector.
sum(A, 2) calculates the sum along the second dimension (column), thus throwing you a column vector with each element the sum of each row.