Until now, the first reported doubly charmed baryon Ξcc+(3520) is still a puzzle. It was discovered and confirmed by SELEX collaboration, but not confirmed by LHCb, BABAR, BELLE, FOCUS, or any other collaboration. In the present paper, by employing Regge phenomenology, we first express the mass of the ground state (L=0) doubly charmed baryon Ωcc∗+
Nearby in the stack
as a function of masses of the well established light baryons and singly charmed baryons. Inserting the recent experimental data, the mass of
Ωcc∗+
is given to be 3809
±
36 MeV, which is independent of any unobservable parameters. Then, with the quadratic mass relations, we calculate the masses of the ground state triply charmed baryon
Ωccc++
and doubly charmed baryons
Ξcc(∗)++
,
Ξcc(∗)+
, and
Ωcc+
(the mass of
Ξcc+
is determined as 3520
−40+41
MeV, which agrees with the mass of
Ξcc+(3520)
). The isospin splitting
MΞcc++−MΞcc+=0.4±0.3
MeV. After that, masses of the orbitally excited (
L
=1,2,3) doubly and triply charmed baryons are estimated. The results are reasonable comparing with those extracted in many other approaches. We suggest more efforts to study doubly and triply charmed baryons both theoretically and experimentally, not only for the abundance of baryon spectra, but also for numerically examining whether the linear mass relations or the quadratic mass relations are realized in nature. Our predictions are useful for the discovery of unobserved doubly and triply charmed baryon states and the