Analysis

This problem tests the general formula of a geometric sequence and its properties, as well as reasoning and computational skills. It is considered a medium-level question.

Solution

Let's assume the common ratio of the geometric sequence $\{a_n\}$, where all terms are positive, is $q > 0$,

Since $a_1=1$ and $a_1+a_3+a_5=21$,

Therefore, $1+q^2+q^4=21$. Solving this equation yields $q=2$.

Then, $a_2+a_4+a_6=q(a_1+a_3+a_5)=2\times21=42$,

Hence, the correct choice is $\boxed{B}$.