  In this paper, we present a new explicit formula for the curvatures of a
regular curve with an arbitrary parameter in the Euclidean space
$\mathbb{R}^n$, $n\geq 2$, expressed only in terms of its derivatives. We
introduce also the notion of tube with arbitrary cross sections around a curve
for which we calculate the volume and give a generalization for the second
theorem of Pappus. The first theorem of Pappus is obtained for sphere tubes in
arbitrary dimension.
