Using adonis2 to consider cage as a random factor in mouse-microbiome study

[shrez28]

We designed a mouse experiment with 4 treatment groups, each consisting of 5 cages, with 3 mice per cage.
To account for the mouse cage as a random factor, we setup the adonis2 analysis as follows:
adonis2(mydist ~ Group+Cage, permutations = 999, method="bray", data = mymetadata, by = "terms")
To block the effect of the mouse cage and check for differences between the 4 groups, we used the following approach
perm <-with(mymetadata, how(nperm=999, blocks=mymetadata$Cage)
adonis2(mydist ~ Group, data = mymetadata, permutations = perm)
Would this be a reasonable approach?