We investigated the U-Ni-B and Nb-Ni-B systems to search for possible new heavy fermion compounds and superconducting materials. The formation, crystal chemistry, and physical properties of U2Ni21B6 and Nb3-yNi20+yB6 [ternary derivatives of the cubic Cr23C6-type (cF116, Fm3m)] have been studied; the formation of the hypothetical "U3Ni20B6" and "Nb2Ni21B6" has been disproved. U2Ni21B6 [a = 10.6701(2) angstrom] crystallizes in the ordered W2Cr21C6-type, whereas Nb3-yNi20+yB6 [a = 10.5842(1) angstrom] adopts the Mg3Ni20B6-type. Ni in U2Ni21B6 can be substituted by U, leading to the solid solution U2-xNi21+yB6 (0 <= x <= 0.3); oppositely, Nb in Nb3Ni20B6 is partially replaced by Ni, forming the solution Nb3-yNi20+yB6 (0 <= y <= 0.5), none of them reaching the limit corresponding to the hypothetically ordered "U3Ni20B6 " and "Nb2Ni21B6". These results prompted us to investigate quaternary compounds U2-zNbzNi21B6 and U6Nb3-delta Ni20B6: strong competition in the occupancy of the 4a and 8c sites by U, Nb, and Ni atoms has been observed, with the 4a site occupied by U/Ni atoms only and the 8c site filled by U/Nb atoms only. U2Ni21B6, U2.3Ni20.7B6, and Nb3Ni20B6 are Pauli paramagnets. Interestingly, Nb2.5Ni20.5B6 shows ferromagnetism with T-c approximate to 11 K; the Curie-Weiss fit gives an effective magnetic moment of 2.78 mu(B)/Ni, suggesting that all Ni atoms in the formula unit contribute to the total magnetic moment. The M(H) data at 2 K further corroborate the ferromagnetic behavior with a saturation moment of 10 mu(B)/fu (approximate to 0.49 mu(B)/Ni). The magnetic moment of Ni at the 4a site induces a moment in all of the Ni atoms of the whole unit cell (32f and 48h sites), with all atoms ordering ferromagnetically at 11 K. Density functional theory (DFT) shows that the formation of U2Ni21B6 and Nb3Ni20B6 is energetically preferred. The various electronic states generating ferromagnetism on Nb2.5Ni20.5B6 and Pauli paramagnetism on U2Ni21B6 and Nb3Ni20B6 have been identified.