SPIRE is an instrument of the Herschel Space Observatory. The Herschel mission ended in 2013, but all the data collected are available from the Herschel Science Archive (HSA). You can download raw to fully reduced SPIRE data. In some cases it will be necessary to partially re-reduce the data, in other cases you can take the pipeline end-products from the HSA and use them for science.
For full details of SPIRE spectroscopic data and how to work with them, check out the various documentation provided on the Herschel/SPIRE web-site (here). If you are going to reduce data you will need to read the SPIRE Data Reduction Guide (available also directly via the Herschel software environment: HIPE), but even if you are only planning to work with the archived and already-reduced data you will find the first chapters of that guide (the Launch Pads) useful. The SPIRE Handbook (aka the SPIRE Observer's Manual) should be consulted for all the technical details of the instrument.
Observing modes and SPIRE cubes
The SPIRE spectrograph (and FTS) was designed to give data from a set of concentric, hexagonally-packed, circular pixels—one spectrum per pixel. These pixels are separated by 33" in the short wavelength band and 51" in the long wavelength band, and their FWHM are a bit smaller. Therefore the pixels are not spatially contiguous: a single pointing results in a set of discrete spectra, usually with the source of interest in the middle and "sky" pixels surrounding that.
By adopting a set of dithering patterns, moving slightly between individual pointings, SPIRE made it possible to build up a denser spectral sampling. The three image samplings were: sparse, intermediate, and full — the latter resulting in Nyquist sampling of the beam. Cubes are the end result ("Level 2" in Herschel-speak) of the intermediate and full sampling modes.
The 3d datasets are created from the individual pointings of the raster pattern by gridding the individual pointings onto a regular sky grid. Different gridding algorithms were created by SPIRE to use in HIPE, some of which use the shape of the beam to help interpolate the data between sky positions, and others doing a more basic averaging of close-by sky positions instead. To learn more about these tasks, consult the various SPIRE documentation (the SPIRE Handbook and the Data Reduction Guide are a good place to start).
SPIRE spectra extend from about 200μm to 670μm in a short and a long wavelength band. You always get the full SED with each observation.
The FITS files
When you download data from the HSA (or if you reduce them yourself in HIPE), the final cubes are FITS files (or can be exported from HIPE as FITS files). The various layers of the cube are contained in separate extensions of the FITS file: the image layer (i.e. the fluxes), as well as the error, coverage, flags, and more. These layers do not have a full WCS associated with them. The spatial dimensions are defined, but the spectral are not.
The spectral dimension of SPIRE data is frequency, and the spectral resolution is either 25 GHz or 1.2 GHz, but given the long wavelength range of the data (over 400μm) it is clear why the spectral sampling, i.e. the dispersion, varies with wavelength. This means that the spectral coordinates of the WCS are not filled, instead the frequencies are included as an extension in the FITS files.
Unfortunately the more complex issues with Herschel FITS files, and a translation of all the SPIRE- and Herschel-specific headers, have not yet (as of April 2014) been nicely documented, but once they are they should be linked from the SPIRE web-site.