Use a shovel to remove the old mailbox. Place the dirt back into the old post hole and level it out. Measure a plot of ground large enough to support the base of the new mailbox. Approximately 16 inches square wil lwork. This is called the footer hole. Dig 8 inches into the ground in this square.
Mix some fast-drying concrete in the wheelbarrow according to the package directions. Place the concrete into the hole until it is filled to ground level. Smooth it with a trowel. Let it dry. Place two 8-inch-by-8 inch-by-16 inch concrete blocks for the base of the mailbox. Use the framing square to line everything up. Mix some more cement. Apply a line of cement everywhere the cement blocks will rest. Press the blocks into place.
Start the second set of bricks for adding height. Outline the bottom layer with cement. Place the second row of bricks perpendicular to the first set. Continue to do this until the box is high enough to place the mailbox on top. This should take about six sets of blocks.
Place a thick bed of cement on top of the mailbox. Place the mailbox on top of the cement. Press it into place. There should be gaps all around the mailbox and the sides of the concrete base. Make sure the mailbox can open completely.
Cut two concrete blocks in half with the circular saw. These will be the sides of the mailbox. Line the top and sides of the mailbox with cement. Press the two sides of the concrete box into the cement around the mailbox. Cut another block in half. Place these two halves on top of the mailbox, completing the square. If you are worried about the appearance of your mailbox, you can use bricks to cover up the cement.