“Well packed” is a bit non-specific. If the cakes are vacuum sealed, in metalized foil, oxygen barrier, and or modified atmosphere, or https://bakerpedia.com/sofresh/ bags, then yes packaging alone can provide what you are aiming for.
Enzymes may be beneficial, but first review your formula and process. Humectant type and proportion? Fat type and proportion? Consistent mixing methods? Bake time and thermal profile?
If everything you are doing is perfect every time, and you still only have 1 month of shelf life, then you may need some enzyme to slow starch retrogradation, known as staling.
A high sugar cake formula, with a significant proportion of fructose and or glycerin, as well as high fat in the formula that is mostly unsaturated fat, that can be packaged sterile, MAP, and vacuum sealed, preferable with an oxygen barrier, will also keep for 3 or more months. Enzymes alone cannot replace all of these items.
You can read more about enzyme functionality here: https://bakerpedia.com/ingredients/enzyme/