To patch or repair concrete you should use a non-shrink grout formulated for that purpose. Cement must be combined with aggregates like sand and gravel and then it is called called grout, mortar, stucco, concrete, etc.

Thanks Renovator8. Is there any products in Home Depot or Lowes I can purchase to patch the wall?

-J

That 2nd pic is just begging for critters to move in. Can you tell if there is something behind it,If possible I would force a piece of metal hardware cloth, animal cage 1/2 by1/2 in screen that is hard to bend something like that & grout over top of that in that wide spot, otherwise your grout has nothing to grip. If possible nail the metal even chicken wire screen in couple of places to hold the grout, if possible bend it so that right side of it goes back to wall behind. If nothing else a piece of aluminum flashing with mesh wrapped around it & nailed to the inside edge of that corner would help hold grout. It won't work to try to put a gob of grout in that big of hole. It needs something to hold on to. Smart to wedge some chicken wire down into other areas that are fairly wide also. The grout will hold if it has something to ooze into.

Thanks all for the replies. Is there foam type of product I can use to seal the small gap? I can find one in HD but it seems for interior use only.

-J

use great stuff - spray foam insulation

Here is a link that might be useful: Great stuff

Animals can easily penetrate foam. Find a non-shrink grout/concrete repair mix, add water, and apply with a trowel.