Specification of linear mixed-effects model

my apologies if this is a very basic question or if similar questions have been asked before. I am relatively new to this kind of modelling and did not find anything yet that resolves my question.

I have an experiment were we count the number of soil insects, expressed as thousands of animals per square meter in our plots. We have four treatments (Control (C), Warming (W), Nutrients (N), Warming and Nutrients (WN)). The four treatments are replicated in 10 Blocks, so each block has all four treatments. Within each block two treatments received herbivore fences (I call it cage), two did not (called control, this was randomly assigned to a treatment within a block). As a result, we have 5 sets of all treatments that had a cage, 5 sets that did not.

My datafile essentially looks like this

    Block   Treatment   Cage       Number
1       C           cage       2.4
1       N           control    5.8
1       W           cage       2.3
1       WN          control    4.1
2       C           control    5.3
....    ....        ....       ....
10      WN          cage       2.7


What I want to know is what effect Treatments have on the number of animals, if caging affects that (interaction), and if there are perhaps differences between the blocks (due to environmental differences, for instance). I plan to use lme4.

Simply, I could specify it like this, with Treatment and Cage as interacting fixed factors, and Block as a random factor:

    model<-lmer(Number ~ Treatment*Cage + (1|Block), data=mydata)


But that would ignore the fact that the Cage treatment is nested within the Blocks. I mean, not all combinations of Cage and Treatment are represented in each block. Is my line of thinking here correct? What are your thoughts on how to capture the design in the model?