Can you add up all the nodes of a special binary tree in polynomial time, in respect to the number of levels?
No.  A complete binary tree has $\ell$ levels and about $2^\ell$ nodes.  Any algorithm must examine all nodes to get the correct answer, so the running time has to be exponential in the number of levels.
(A small note of caution: &quot;polynomial time&quot; typically means polynomial in the size of the input, so it could risk some confusion to talk about it as &quot;polynomial time&quot; when you mean a polynomial in the number of levels.)