We report magnetization experiments in two magnetically isolated ferromagnetic nanotubes of perovskite La_0.67Ca_0.33MnO₃. The results show that the magnetic anisotropy is determined by the sample shape, although the coercive field is reduced by incoherent magnetization reversal modes. The temperature dependence of the magnetization reveals that the magnetic behavior is dominated by grain surface properties. These measurements were acquired using a silicon micromechanical oscillator working in its resonant mode. The sensitivity was enough to measure the magnetic properties of these two samples with a mass lower than 14.pg and to obtain for the first time the magnetization loop for one isolated nanotube.