The permanent of a matrix is defined similarly to the determinant, only differing in that the signatures of the permutations are not considered. Both matrix functions share common properties, but the multiplicative property of determinants does not hold for permanents. It should be stressed that the evaluation of permanents is in general very difficult. This paper is concerned with the computation of permanents of block matrices in terms of the entries of each block. In this setup a formula is derived, and using it a generalized Lieb permanent inequality on positive semi-definite block matrices is obtained.