"By March next" sounds wrong to me. To check whether this is a Britishism or some variation of English that I'm not familiar with, I've done a Google search for "By March next, we". The result was just over a thousand entries, most of which seem to be in Asian publications. Unless you're in a country where you hear people speak this way, it's probably best to go with "by next March" or "by March next year".
We will/shall have finished our work by next March.
Our work will have been finished by us by next March.
By next March, our work will have been finished by us.
These three sentences are all grammatically correct and mean the same thing, but only the first sentence sounds natural. The only reason I can imagine for choosing the passive voice here is to avoid specifying who will do the work. In this case, however, one would leave out "by us":
Our work will have been finished by next March.
By next March, our work will have been finished.
In the absence of a strong reason to use the passive voice, it's usually best to stick to the active voice.