1. Use the standard result:
   The sum of all coefficients of a polynomial $P(x)$ is obtained by putting $x=1$.

2. Find $A$:
   Given $A=\text{sum of coefficients of }(1-3x+10x^2)^n$ So, $A=(1-3\cdot 1+10\cdot 1^2)^n=(1-3+10)^n=8^n$

3. Find $B$:
   Given $B=\text{sum of coefficients of }(1+x^2)^n$ So, $B=(1+1^2)^n=(1+1)^n=2^n$

4. Compare $A$ and $B$:
   We have $A=8^n=(2^3)^n=2^{3n}=(2^n)^3=B^3$

   Hence, $A=B^3$

5. Check options:

   • A: $B=A^3$ is false
   • B: $3A=B$ is false
   • C: $A=3B$ is false
   • D: $A=B^3$ is true

Therefore, the correct option is D.