Summary: Muscle density is 1.06 g/ml and fat density is (about) 0.9
g/ml.
Thus, one liter of muscle would weight 1.06 kg and one liter of
fat would weight 0.9 kg.
In other words, muscle is about 18% denser than fat.
This should not be confused with the "energy density" of
muscle and fat, which may be where you got the 3x figure that you
mention in your question.
I have made a special effort to find credible sources for the answer.
Below I provide sources for the two numbers separately.
1. The density of mammalian skeletal muscle is 1.06 g/ml.
"... 1.06 g/cm-3 which is the density of mammalian skeletal muscle"
Source for quote: The Journals of Gerontology Series A: Biological
Sciences and Medical Sciences 56:B191-B197 (2001)
Specific Force Deficit in Skeletal Muscles of Old Rats Is Partially
Explained by the Existence of Denervated Muscle Fibers
Melanie G. Urbancheka, Elisa B. Pickenb, Loree K. Kalliainenc and
William M. Kuzon, Jr.a,d
http://biomed.gerontologyjournals.org/cgi/content/full/56/5/B191#R23
Reference given by the authors: Mendez J, Keys A, 1960. Density and
composition of mammalian muscle. Metabolism 9:184-188.
2. The density of adipose tissue (fat) is about 0.9 g/ml
"...by multiplying the density of adipose tissue (0.9196 g/ml)"
Source: Association of adiponectin and resistin with adipose tissue
compartments, insulin resistance and dyslipidaemia
M. S. Farvid1, T. W. K. Ng2, D. C. Chan2, P. H. R. Barrett2 and G. F. Watts2*
http://www.blackwell-synergy.com/doi/abs/10.1111/j.1463-1326.2004.00410.x
"...on the assumption that the density of adipose tissue is 0.9g/cm3"
Source of quote: Pediatric Research 55:437-441 (2004)
Distribution of Adipose Tissue in the Newborn
TRACEY A.M. HARRINGTON, ELIZABETH LOUISE THOMAS, GARY FROST, NEENA
MODI and JIMMY D. BELL
Source given by authors:
Ross R, Léger L, Guardo R, De Guise J, Pike BG 1991 Adipose tissue
volume measured by magnetic resonance imaging and computerized
tomography in rats. J Appl Physiol 70: 2164?2172