This paper brings idea how we can organize block-wise constructions of magic and bimagic squares. This we have done for the magic squares of orders 8 to 108. By use of the formula for the calculations of magic squares, we can check the existence of blocks of equal or unequal sums. In case of blocks of order 3, either we have equal sums of semi-magic blocks or unequal blocks of magic squares of order 3. While, in case of blocks of order 4, 5 and 7, the magic squares can be written as pandiagonal. For the case of blocks of order 6, the blocks are of equal magic sums, but the magic squares are not pandiagonal.