Sq10bit:   ;input in r0,r1; output in r2,r3,r4; both LSB first
   mov  a,r0    ;(a+b)^2=a^2+2*a*b+b^2
   mov  b,a
   mul  ab
   mov  r2,a
   mov  r3,b
   mov  a,r1
   mov  b,a
   mul  ab
   mov  r4,a
   mov  a,r1
   add  a,r1
   mov  b,r0
   mul  ab
   add  a,r3
   mov  r3,a
   mov  a,b
   addc a,r4
   mov  r4,a
   ret

23 bytes, 31 cycles including RET, uses only a,b and flags. Could be tweaked a bit more, but don't expect much less. R0-R4 can be replaced by memory positions, but then expect longer code and execution time.
Intentionally not commented. Try to understand yourself. Have fun!

Jan Waclawek