Definitely! Stale wholemeal bread makes a very good mouse food, and lots of show mice live on very little else. Some fanciers say that it should be allowed to dry out thoroughly first, then soak it in water (or skimmed milk for babies/mothers, or stock/gravy for a change of flavor).
The reason for allowing the bread to go stale first is that some mice apparently react badly to enzymes in fresh bread which are killed by the staling process, getting spots as a result. I have not experienced this personally, and frequently feed fresh bread to my mice without problems.
Happy breading feeding to your little ones!
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