Preparation
The preparation of diethyl 1,1-cyclobutanedicarboxylate is as follows:The major product is tetraethy1 1,1,5,5-pentanetetra-carboxylate II with diethyl malonate. To eliminate this side reaction, II was independently prepared by the addition of hydrogen bromide to diethyl allylmalonate (I) and then cyclized to II by treatment with sodium ethylate. The over-all yield from I is about 50%.

Synthesis
GENERAL METHOD: Diethyl malonate (2.53 mL, 17 mmol), 1,3-dibromopropane (22 mmol), potassium carbonate (K2CO3, 5.7 g, 42 mmol) and tetrabutylammonium bromide (TBAB, 0.27 g, 0.08 mmol) were added to dry N,N-dimethylformamide (DMF). The reaction mixture was stirred at room temperature for 16 hours. After completion of the reaction, the solvent was removed by rotary evaporator and the residue was extracted three times with ethyl acetate (100 mL). The organic layers were combined, washed with water and then dried over anhydrous sodium sulfate. After filtration, the filtrate was concentrated to give diethyl cyclobutyl-1,1-dicarboxylate as a colorless oil (89% yield).
References
[1] Molecules, 2016, vol. 21, # 5,
[2] Journal of Organic Chemistry, 1993, vol. 58, # 27, p. 7709 - 7717
[3] Journal of Fluorine Chemistry, 2000, vol. 102, # 1-2, p. 141 - 146
[4] Journal of Organic Chemistry, 1949, vol. 14, p. 1036
[5] Journal of the Chemical Society, 1887, vol. 51, p. 2