First, perform the multiplication of the first two terms:

(13+3i)(13+3i) = 169 + 39i + 39i + 9i^2
= 169 + 78i - 9
= 160 + 78i

Now, multiply this result by the third term:

(160 + 78i)(17+3i) = 160(17) + 160(3i) + 78i(17) + 78i(3i)
= 2720 + 480i + 1326i + 234i^2
= 2720 + 1806i - 234
= 2486 + 1806i

Therefore, (13+3i)(13+3i)(17+3i) = 2486 + 1806i.