Yep, I'm sure. For example,
111*111 = (1+10+100) * (1+10+100) =
(1*1) + (1*10 + 10*1) + (1*100 + 10*10 + 100*1) + (10*100 + 100*10) + (100*100) =
1*1 + 2*10 + 3*100 + 2*1000 + 1*10000 = 12321
Plus I checked it on a calculator xD
Now, knowing me, I'll probably spend the rest of the day trying...