In this paper, we derive the Cramer-Rao bound (CRB) for data-aided channel estimation for OFDM with known symbol padding (KSP-OFDM). The pilot symbols used to estimate the channel are distributed over the guard interval and OFDM carriers, in order to keep the guard interval length as small as possible. An analytical expression for the CRB is obtained by performing a proper linear transformation on the observed samples. At low SNR, the CRB corresponds to the low SNR limit of the CRB obtained in [1], where it is assumed that the influence of the data symbols on the channel estimation can be neglected. At high SNR, the CRB is determined by the observations that are independent of the data symbols; the observations that are affected by data symbols are neglected. The CRB depends on the number of pilots and slightly increases with increasing guard interval length, but is essentially independent of the FFT size and the used pilot sequence. Further, a low complexity ML channel estimation technique is derived based on the linear transformation. Although in this estimation technique only a part of the observation is used, the mean squared error (MSE) performance of this estimate reaches the CRB for a large range of SNR, but a high SNR, the MSE reaches an error floor caused by the approximations made in the derivation.