Yes, absolutely you can. However, you may need to make adjustments.
First, there's water content. Palm sugar has a relatively high water content out of the cake, almost 4%. That's compared to less than 2% for brown sugar, and about 0.4% for white granulated sugar. So you'll need to adjust the water content of your recipes accordingly.
Also, palm sugar won't brown the same way other sugars do. Particularly, white granulated sugar is good for crispy baked goods because it melts well without giving off water, and you won't expect that effect from palm sugar. Further, since you generally need to grate palm sugar yourself, it won't have the large crystals like granulated sugar does.
Overall, I'd suggest that you'd get the best results substituting palm sugar into recipes that call for brown sugar, and otherwise into recipes for cakes, rolls, muffins, and similar things that don't rely on the sugar's texture.