Density functional calculations are used to determine structures and stabilities of cages P-20 and P20O20 and their endohedral complexes Na@P-20, Na+@P20Na@P20O20, and Na-@P20O20. Calculations show that the cages P-20 and P20O20 are composed of sigma bonds and they have no spherical aromaticity unlike fullerene. Predicted first ionization potential of the endohedral complex Na@P-20 is 6.04 eV, higher than 5.36 eV of the isolated Na atom. The electron binding energy of the endohedral complex Na-@P20O20 is 6.39 eV, suggesting that Na@P20O20 has much higher electron affinity energy than the F atom with the largest elementary electronegativity Value. Such Outstanding features of the encaged Na species arise from the electrostatic and donor(-)acceptor interactions between the capsulated species and the cages P-20 with the sigma-bond network and P20O20 with the spherical double electric layer. Such novel molecular cages can selectively trap atoms and ions inside and outside, and they may have practical uses as potential building units of nanoscale materials.