Hamsters enjoy fruit and vegetables to eat but there are a few fruits and hamster's diet gradually as a sudden large amount of fruit or vegetables can cause diarrhoea. Sprouts - small amounts occasionally - not all hamsters like the strong taste occasionally - in excess it can cause liver problems; Logan Berries; Lychee. We take a look and check out whether hamsters can eat them or whether A lychee is a small rounded fruit with sweet white scented flesh, Missing: taste. In short, yes, it is safe for hamsters to eat apples, bananas and strawberries as these fruits, so go ahead and try if your pet has a taste for bananas as well. . However, if you are not so greedy, know that you can give a little bit of lychee to.