  Subspace codes, especially cyclic constant subspace codes, are of great use
in random network coding. Subspace codes can be constructed by subspaces and
subspace polynomials. In particular, many researchers are keen to find special
subspaces and subspace polynomials to construct subspace codes with the size
and the minimum distance as large as possible. In [14], Roth, Raviv and Tamo
constructed several subspace codes using Sidon spaces, and it is proved that
subspace codes constructed by Sidon spaces has the largest size and minimum
distance. In [12], Niu, Yue and Wu extended some results of [14] and obtained
several new subspace codes. In this paper, we first provide a sufficient
condition for the sum of Sidon spaces is again a Sidon space. Based on this
result, we obtain new cyclic constant subspace codes through the sum of two and
three Sidon spaces. Our results generalize the results in [14] and [12].
