I don't know what I'm doing wrong, but all my babyfood cubes are getting freezer burn.

I have ice cube trays with lids, and then after freezing, I transfer to freezer bags, but the cubes are still getting freezer burn inside the bags. Anyone else have this problem? I bought the Ziploc brand freezer bags, so it's not like they are cheap generic ones, so I don't know why I'm still getting freezer burn. Any thoughts?
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Re: How to prevent freezer burn on homemade babyfood cubes?
I suck at freezing anything--but have you sucked the air out of the bag??
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Notes:
Only some of mine seem to be getting freezer burn too (the peas in particular), and I have no idea why... but I also don't really care. My suggestion would be to make smaller batches so you don't have quite so much extra to still so long in your fridge.
I could be totally wrong, but I didn't think freezer burn actually does anything to these cubes. I know it effects meat, but not for fruit/veggies.